This file is indexed.

/usr/share/octave/packages/signal-1.3.2/doc-cache is in octave-signal 1.3.2-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

   1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
4513
4514
4515
4516
4517
4518
4519
4520
4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
4532
4533
4534
4535
4536
4537
4538
4539
4540
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555
4556
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
4580
4581
4582
4583
4584
4585
4586
4587
4588
4589
4590
4591
4592
4593
4594
4595
4596
4597
4598
4599
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
4621
4622
4623
4624
4625
4626
4627
4628
4629
4630
4631
4632
4633
4634
4635
4636
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
5236
5237
5238
5239
5240
5241
5242
5243
5244
5245
5246
5247
5248
5249
5250
5251
5252
5253
5254
5255
5256
5257
5258
5259
5260
5261
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
5277
5278
5279
5280
5281
5282
5283
5284
5285
5286
5287
5288
5289
5290
5291
5292
5293
5294
5295
5296
5297
5298
5299
5300
5301
5302
5303
5304
5305
5306
5307
5308
5309
5310
5311
5312
5313
5314
5315
5316
5317
5318
5319
5320
5321
5322
5323
5324
5325
5326
5327
5328
5329
5330
5331
5332
5333
5334
5335
5336
5337
5338
5339
5340
5341
5342
5343
5344
5345
5346
5347
5348
5349
5350
5351
5352
5353
5354
5355
5356
5357
5358
5359
5360
5361
5362
5363
5364
5365
5366
5367
5368
5369
5370
5371
5372
5373
5374
5375
5376
5377
5378
5379
5380
5381
5382
5383
5384
5385
5386
5387
5388
5389
5390
5391
5392
5393
5394
5395
5396
5397
5398
5399
5400
5401
5402
5403
5404
5405
5406
5407
5408
5409
5410
5411
5412
5413
5414
5415
5416
5417
5418
5419
5420
5421
5422
5423
5424
5425
5426
5427
5428
5429
5430
5431
5432
5433
5434
5435
5436
5437
5438
5439
5440
5441
5442
5443
5444
5445
5446
5447
5448
5449
5450
5451
5452
5453
5454
5455
5456
5457
5458
5459
5460
5461
5462
5463
5464
5465
5466
5467
5468
5469
5470
5471
5472
5473
5474
5475
5476
5477
5478
5479
5480
5481
5482
5483
5484
5485
5486
5487
5488
5489
5490
5491
5492
5493
5494
5495
5496
5497
5498
5499
5500
5501
5502
5503
5504
5505
5506
5507
5508
5509
5510
5511
5512
5513
5514
5515
5516
5517
5518
5519
5520
5521
5522
5523
5524
5525
5526
5527
5528
5529
5530
5531
5532
5533
5534
5535
5536
5537
5538
5539
5540
5541
5542
5543
5544
5545
5546
5547
5548
5549
5550
5551
5552
5553
5554
5555
5556
5557
5558
5559
5560
5561
5562
5563
5564
5565
5566
5567
5568
5569
5570
5571
5572
5573
5574
5575
5576
5577
5578
5579
5580
5581
5582
5583
5584
5585
5586
5587
5588
5589
5590
5591
5592
5593
5594
5595
5596
5597
5598
5599
5600
5601
5602
5603
5604
5605
5606
5607
5608
5609
5610
5611
5612
5613
5614
5615
5616
5617
5618
5619
5620
5621
5622
5623
5624
5625
5626
5627
5628
5629
5630
5631
5632
5633
5634
5635
5636
5637
5638
5639
5640
5641
5642
5643
5644
5645
5646
5647
5648
5649
5650
5651
5652
5653
5654
5655
5656
5657
5658
5659
5660
5661
5662
5663
5664
5665
5666
5667
5668
5669
5670
5671
5672
5673
5674
5675
5676
5677
5678
5679
5680
5681
5682
5683
5684
5685
5686
5687
5688
5689
5690
5691
5692
5693
5694
5695
5696
5697
5698
5699
5700
5701
5702
5703
5704
5705
5706
5707
5708
5709
5710
5711
5712
5713
5714
5715
5716
5717
5718
5719
5720
5721
5722
5723
5724
5725
5726
5727
5728
5729
5730
5731
5732
5733
5734
5735
5736
5737
5738
5739
5740
5741
5742
5743
5744
5745
5746
5747
5748
5749
5750
5751
5752
5753
5754
5755
5756
5757
5758
5759
5760
5761
5762
5763
5764
5765
5766
5767
5768
5769
5770
5771
5772
5773
5774
5775
5776
5777
5778
5779
5780
5781
5782
5783
5784
5785
5786
5787
5788
5789
5790
5791
5792
5793
5794
5795
5796
5797
5798
5799
5800
5801
5802
5803
5804
5805
5806
5807
5808
5809
5810
5811
5812
5813
5814
5815
5816
5817
5818
5819
5820
5821
5822
5823
5824
5825
5826
5827
5828
5829
5830
5831
5832
5833
5834
5835
5836
5837
5838
5839
5840
5841
5842
5843
5844
5845
5846
5847
5848
5849
5850
5851
5852
5853
5854
5855
5856
5857
5858
5859
5860
5861
5862
5863
5864
5865
5866
5867
5868
5869
5870
5871
5872
5873
5874
5875
5876
5877
5878
5879
5880
5881
5882
5883
5884
5885
5886
5887
5888
5889
5890
5891
5892
5893
5894
5895
5896
5897
5898
5899
5900
5901
5902
5903
5904
5905
5906
5907
5908
5909
5910
5911
5912
5913
5914
5915
5916
5917
5918
5919
5920
5921
5922
5923
5924
5925
5926
5927
5928
5929
5930
5931
5932
5933
5934
5935
5936
5937
5938
5939
5940
5941
5942
5943
5944
5945
5946
5947
5948
5949
5950
5951
5952
5953
5954
5955
5956
5957
5958
5959
5960
5961
5962
5963
5964
5965
5966
5967
5968
5969
5970
5971
5972
5973
5974
5975
5976
5977
5978
5979
5980
5981
5982
5983
5984
5985
5986
5987
5988
5989
5990
5991
5992
5993
5994
5995
5996
5997
5998
5999
6000
6001
6002
6003
6004
6005
6006
6007
6008
6009
6010
6011
6012
6013
6014
6015
6016
6017
6018
6019
6020
6021
6022
6023
6024
6025
6026
6027
6028
6029
6030
6031
6032
6033
6034
6035
6036
6037
6038
6039
6040
6041
6042
6043
6044
6045
6046
6047
6048
6049
6050
6051
6052
6053
6054
6055
6056
6057
6058
6059
6060
6061
6062
6063
6064
6065
6066
6067
6068
6069
6070
6071
6072
6073
6074
6075
6076
6077
6078
6079
6080
6081
6082
6083
6084
6085
6086
6087
6088
6089
6090
6091
6092
6093
6094
6095
6096
6097
6098
6099
6100
6101
6102
6103
6104
6105
6106
6107
6108
6109
6110
6111
6112
6113
6114
6115
6116
6117
6118
6119
6120
6121
6122
6123
6124
6125
6126
6127
6128
6129
6130
6131
6132
6133
6134
6135
6136
6137
6138
6139
6140
6141
6142
6143
6144
6145
6146
6147
6148
6149
6150
6151
6152
6153
6154
6155
6156
6157
6158
6159
6160
6161
6162
6163
6164
6165
6166
6167
6168
6169
6170
6171
6172
6173
6174
6175
6176
6177
6178
6179
6180
6181
6182
6183
6184
6185
6186
6187
6188
6189
6190
6191
6192
6193
6194
6195
6196
6197
6198
6199
6200
6201
6202
6203
6204
6205
6206
6207
6208
6209
6210
6211
6212
6213
6214
6215
6216
6217
6218
6219
6220
6221
6222
6223
6224
6225
6226
6227
6228
6229
6230
6231
6232
6233
6234
6235
6236
6237
6238
6239
6240
# doc-cache created by Octave 4.0.0
# name: cache
# type: cell
# rows: 3
# columns: 145
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
ar_psd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4030
 -- Function File: ar_psd (A, V)
 -- Function File: ar_psd (A, V, FREQ)
 -- Function File: ar_psd (A, V, FREQ, FS)
 -- Function File: ar_psd (..., RANGE)
 -- Function File: ar_psd (..., METHOD)
 -- Function File: ar_psd (..., PLOTTYPE)
 -- Function File: [PSD, F_OUT] = ar_psd (...)

     Calculate the power spectrum of the autoregressive model

                                 M
          x(n) = sqrt(v).e(n) + SUM a(k).x(n-k)
                                k=1

     where x(n) is the output of the model and e(n) is white noise.
     This function is intended for use with '[a, v, k] = arburg (x,
     poles, criterion)' which use the Burg (1968) method to calculate a
     "maximum entropy" autoregressive model of X.

     If the FREQ argument is a vector (of frequencies) the spectrum is
     calculated using the polynomial method and the METHOD argument is
     ignored.  For scalar FREQ, an integer power of 2, or METHOD =
     "FFT", causes the spectrum to be calculated by FFT. Otherwise, the
     spectrum is calculated as a polynomial.  It may be computationally
     more efficient to use the FFT method if length of the model is not
     much smaller than the number of frequency values.  The spectrum is
     scaled so that spectral energy (area under spectrum) is the same as
     the time-domain energy (mean square of the signal).

     ARGUMENTS: All but the first two arguments are optional and may be
     empty.
        * A list of M=(order+1) autoregressive model coefficients.  The
          first element of "ar_coeffs" is the zero-lag coefficient,
          which always has a value of 1.
        * V square of the moving-average coefficient of the AR model.
        * FREQ frequencies at which power spectral density is
          calculated, or a scalar indicating the number of uniformly
          distributed frequency values at which spectral density is
          calculated.  (default = 256)
        * FS sampling frequency (Hertz) (default=1)

     CONTROL-STRING ARGUMENTS - each of these arguments is a character
     string.  Control-string arguments can be in any order after the
     other arguments.

     Range:

     'half', 'onesided' : frequency range of the spectrum is from zero
     up to but not including sample_f/2.  Power from negative
     frequencies is added to the positive side of the spectrum.
     'whole', 'twosided' : frequency range of the spectrum is
     -sample_f/2 to sample_f/2, with negative frequencies stored in
     "wrap around" order after the positive frequencies; e.g.
     frequencies for a 10-point 'twosided' spectrum are 0 0.1 0.2 0.3
     0.4 0.5 -0.4 -0.3 -0.2 -0.1 'shift', 'centerdc' : same as 'whole'
     but with the first half of the spectrum swapped with second half to
     put the zero-frequency value in the middle.  (See "help fftshift".
     If "freq" is vector, 'shift' is ignored.  If model coefficients
     "ar_coeffs" are real, the default range is 'half', otherwise
     default range is 'whole'.

     Method:

     'fft': use FFT to calculate power spectrum.  'poly': calculate
     power spectrum as a polynomial of 1/z N.B. this argument is ignored
     if the "freq" argument is a vector.  The default is 'poly' unless
     the "freq" argument is an integer power of 2.

     Plot type:

     'plot', 'semilogx', 'semilogy', 'loglog', 'squared' or 'db':
     specifies the type of plot.  The default is 'plot', which means
     linear-linear axes.  'squared' is the same as 'plot'.  'dB' plots
     "10*log10(psd)".  This argument is ignored and a spectrum is not
     plotted if the caller requires a returned value.

     RETURNED VALUES: If returned values are not required by the caller,
     the spectrum is plotted and nothing is returned.
        * PSD estimate of power-spectral density
        * F_OUT frequency values

     REFERENCE [1] Equation 2.28 from Steven M. Kay and Stanley Lawrence
     Marple Jr.: "Spectrum analysis - a modern perspective", Proceedings
     of the IEEE, Vol 69, pp 1380-1419, Nov., 1981


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
Calculate the power spectrum of the autoregressive model



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
arburg


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3775
 -- Function File: [A, V, K] = arburg (X, POLES)
 -- Function File: [A, V, K] = arburg (X, POLES, CRITERION)

     Calculate coefficients of an autoregressive (AR) model of complex
     data X using the whitening lattice-filter method of Burg (1968).
     The inverse of the model is a moving-average filter which reduces X
     to white noise.  The power spectrum of the AR model is an estimate
     of the maximum entropy power spectrum of the data.  The function
     'ar_psd' calculates the power spectrum of the AR model.

     ARGUMENTS:
        * X sampled data
        * POLES number of poles in the AR model or limit to the number
          of poles if a valid CRITERION is provided.
        * CRITERION model-selection criterion.  Limits the number of
          poles so that spurious poles are not added when the whitened
          data has no more information in it (see Kay & Marple, 1981).
          Recognized values are 'AKICc' - approximate corrected Kullback
          information criterion (recommended), 'KIC' - Kullback
          information criterion 'AICc' - corrected Akaike information
          criterion 'AIC' - Akaike information criterion 'FPE' - final
          prediction error" criterion The default is to NOT use a
          model-selection criterion

     RETURNED VALUES:
        * A list of (P+1) autoregression coefficients; for data input
          x(n) and white noise e(n), the model is

                                     P+1
               x(n) = sqrt(v).e(n) + SUM a(k).x(n-k)
                                     k=1

          V mean square of residual noise from the whitening operation
          of the Burg lattice filter.
        * K reflection coefficients defining the lattice-filter
          embodiment of the model

     HINTS:

     (1) arburg does not remove the mean from the data.  You should
     remove the mean from the data if you want a power spectrum.  A
     non-zero mean can produce large errors in a power-spectrum
     estimate.  See "help detrend".  (2) If you don't know what the
     value of "poles" should be, choose the largest (reasonable) value
     you could want and use the recommended value, criterion='AKICc', so
     that arburg can find it.  E.g.  arburg(x,64,'AKICc') The AKICc has
     the least bias and best resolution of the available model-selection
     criteria.  (3) Autoregressive and moving-average filters are stored
     as polynomials which, in matlab, are row vectors.

     NOTE ON SELECTION CRITERION:

     AIC, AICc, KIC and AKICc are based on information theory.  They
     attempt to balance the complexity (or length) of the model against
     how well the model fits the data.  AIC and KIC are biased estimates
     of the asymmetric and the symmetric Kullback-Leibler divergence
     respectively.  AICc and AKICc attempt to correct the bias.  See
     reference [4].

     REFERENCES:

     [1] John Parker Burg (1968) "A new analysis technique for time
     series data", NATO advanced study Institute on Signal Processing
     with Emphasis on Underwater Acoustics, Enschede, Netherlands, Aug.
     12-23, 1968.

     [2] Steven M. Kay and Stanley Lawrence Marple Jr.: "Spectrum
     analysis - a modern perspective", Proceedings of the IEEE, Vol 69,
     pp 1380-1419, Nov., 1981

     [3] William H. Press and Saul A. Teukolsky and William T.
     Vetterling and Brian P. Flannery "Numerical recipes in C, The art
     of scientific computing", 2nd edition, Cambridge University Press,
     2002 -- Section 13.7.

     [4] Abd-Krim Seghouane and Maiza Bekara "A small sample model
     selection criterion based on Kullback's symmetric divergence", IEEE
     Transactions on Signal Processing, Vol.  52(12), pp 3314-3323, Dec.
     2004

     See also: ar_psd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Calculate coefficients of an autoregressive (AR) model of complex data X
using t



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
aryule


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 934
 -- Function File: A = aryule (X, P)
 -- Function File: [A, V, K] = aryule (X, P)
     Fit an AR (P)-model with Yule-Walker estimates.
     X
          data vector to estimate
     A
          AR coefficients
     V
          variance of white noise
     K
          reflection coefficients for use in lattice filter

     The power spectrum of the resulting filter can be plotted with
     pyulear(x, p), or you can plot it directly with ar_psd(a,v,...).

     See also: pyulear, power, freqz, impz - for observing
     characteristics of the model arburg - for alternative spectral
     estimators

     Example: Use example from arburg, but substitute aryule for arburg.

     Note: Orphanidis '85 claims lattice filters are more tolerant of
     truncation errors, which is why you might want to use them.
     However, lacking a lattice filter processor, I haven't tested that
     the lattice filter coefficients are reasonable.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Fit an AR (P)-model with Yule-Walker estimates.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
barthannwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 158
 -- Function File: barthannwin (M)
     Return the filter coefficients of a modified Bartlett-Hann window
     of length M.

     See also: rectwin, bartlett.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 78
Return the filter coefficients of a modified Bartlett-Hann window of
length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
besselap


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 168
 -- Function File: [ZERO, POLE, GAIN] = besselap (N)
     Return bessel analog filter prototype.

     References:

     http://en.wikipedia.org/wiki/Bessel_polynomials


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Return bessel analog filter prototype.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
besself


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 879
 -- Function File: [B, A] = besself (N, W)
 -- Function File: [B, A] = besself (N, W, "high")
 -- Function File: [Z, P, G] = besself (...)
 -- Function File: [A, B, C, D] = besself (...)
 -- Function File: [...] = besself (..., "z")
     Generate a Bessel filter.  Default is a Laplace space (s) filter.

     [b,a] = besself(n, Wc) low pass filter with cutoff pi*Wc radians

     [b,a] = besself(n, Wc, 'high') high pass filter with cutoff pi*Wc
     radians

     [z,p,g] = besself(...)  return filter as zero-pole-gain rather than
     coefficients of the numerator and denominator polynomials.

     [...]  = besself(...,'z') return a discrete space (Z) filter, W
     must be less than 1.

     [a,b,c,d] = besself(...)  return state-space matrices

     References:

     Proakis & Manolakis (1992).  Digital Signal Processing.  New York:
     Macmillan Publishing Company.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Generate a Bessel filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
bilinear


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2955
 -- Function File: [ZB, ZA] = bilinear (SB, SA, T)
 -- Function File: [ZB, ZA] = bilinear (SZ, SP, SG, T)
 -- Function File: [ZZ, ZP, ZG] = bilinear (...)
     Transform a s-plane filter specification into a z-plane
     specification.  Filters can be specified in either zero-pole-gain
     or transfer function form.  The input form does not have to match
     the output form.  1/T is the sampling frequency represented in the
     z plane.

     Note: this differs from the bilinear function in the signal
     processing toolbox, which uses 1/T rather than T.

     Theory: Given a piecewise flat filter design, you can transform it
     from the s-plane to the z-plane while maintaining the band edges by
     means of the bilinear transform.  This maps the left hand side of
     the s-plane into the interior of the unit circle.  The mapping is
     highly non-linear, so you must design your filter with band edges
     in the s-plane positioned at 2/T tan(w*T/2) so that they will be
     positioned at w after the bilinear transform is complete.

     The following table summarizes the transformation:

          +---------------+-----------------------+----------------------+
          | Transform     | Zero at x             | Pole at x            |
          |    H(S)       |   H(S) = S-x          |    H(S)=1/(S-x)      |
          +---------------+-----------------------+----------------------+
          |       2 z-1   | zero: (2+xT)/(2-xT)   | zero: -1             |
          |  S -> - ---   | pole: -1              | pole: (2+xT)/(2-xT)  |
          |       T z+1   | gain: (2-xT)/T        | gain: (2-xT)/T       |
          +---------------+-----------------------+----------------------+

     With tedious algebra, you can derive the above formulae yourself by
     substituting the transform for S into H(S)=S-x for a zero at x or
     H(S)=1/(S-x) for a pole at x, and converting the result into the
     form:

             H(Z)=g prod(Z-Xi)/prod(Z-Xj)

     Please note that a pole and a zero at the same place exactly
     cancel.  This is significant since the bilinear transform creates
     numerous extra poles and zeros, most of which cancel.  Those which
     do not cancel have a "fill-in" effect, extending the shorter of the
     sets to have the same number of as the longer of the sets of poles
     and zeros (or at least split the difference in the case of the band
     pass filter).  There may be other opportunistic cancellations but I
     will not check for them.

     Also note that any pole on the unit circle or beyond will result in
     an unstable filter.  Because of cancellation, this will only happen
     if the number of poles is smaller than the number of zeros.  The
     analytic design methods all yield more poles than zeros, so this
     will not be a problem.

     References:

     Proakis & Manolakis (1992).  Digital Signal Processing.  New York:
     Macmillan Publishing Company.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 70
Transform a s-plane filter specification into a z-plane specification.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
bitrevorder


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 239
 -- Function File: Y = bitrevorder (X)
 -- Function File: [Y I] = bitrevorder (X)
     Reorder the elements of the vector X in bit-reversed order.
     Equivalent to calling 'digitrevorder (X, 2)'.

     See also: digitrevorder, fft, ifft.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
Reorder the elements of the vector X in bit-reversed order.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
blackmanharris


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 545
 -- Function File: blackmanharris (M)
 -- Function File: blackmanharris (M, "periodic")
 -- Function File: blackmanharris (M, "symmetric")
     Return the filter coefficients of a Blackman-Harris window of
     length M.

     If the optional argument '"periodic"' is given, the periodic form
     of the window is returned.  This is equivalent to the window of
     length M+1 with the last coefficient removed.  The optional
     argument '"symmetric"' is equivalent to not specifying a second
     argument.

     See also: rectwin, bartlett.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 71
Return the filter coefficients of a Blackman-Harris window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
blackmannuttall


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 550
 -- Function File: blackmannuttall (M)
 -- Function File: blackmannuttall (M, "periodic")
 -- Function File: blackmannuttall (M, "symmetric")
     Return the filter coefficients of a Blackman-Nuttall window of
     length M.

     If the optional argument '"periodic"' is given, the periodic form
     of the window is returned.  This is equivalent to the window of
     length M+1 with the last coefficient removed.  The optional
     argument '"symmetric"' is equivalent to not specifying a second
     argument.

     See also: nuttallwin, kaiser.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
Return the filter coefficients of a Blackman-Nuttall window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
bohmanwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 135
 -- Function File: bohmanwin (M)
     Return the filter coefficients of a Bohman window of length M.

     See also: rectwin, bartlett.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Return the filter coefficients of a Bohman window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
boxcar


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 102
 -- Function File: boxcar (M)
     Return the filter coefficients of a rectangular window of length M.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
Return the filter coefficients of a rectangular window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
buffer


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1490
 -- Function File: Y = buffer (X, N, P, OPT)
 -- Function File: [Y, Z, OPT] = buffer (...)
     Buffer a signal into a data frame.  The arguments to 'buffer' are

     X
          The data to be buffered.

     N
          The number of rows in the produced data buffer.  This is an
          positive integer value and must be supplied.

     P
          An integer less than N that specifies the under- or overlap
          between column in the data frame.  The default value of P is
          0.

     OPT
          In the case of an overlap, OPT can be either a vector of
          length P or the string 'nodelay'.  If OPT is a vector, then
          the first P entries in Y will be filled with these values.  If
          OPT is the string 'nodelay', then the first value of Y
          corresponds to the first value of X.

          In the can of an underlap, OPT must be an integer between 0
          and '-P'.  The represents the initial underlap of the first
          column of Y.

          The default value for OPT the vector 'zeros (1, P)' in the
          case of an overlap, or 0 otherwise.

     In the case of a single output argument, Y will be padded with
     zeros to fill the missing values in the data frame.  With two
     output arguments Z is the remaining data that has not been used in
     the current data frame.

     Likewise, the output OPT is the overlap, or underlap that might be
     used for a future call to 'code' to allow continuous buffering.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
Buffer a signal into a data frame.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
buttap


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
 -- Function File: [Z, P, G] = buttap (N)
     Design lowpass analog Butterworth filter.

     This function exists for MATLAB compatibility only, and is
     equivalent to 'butter (N, 1, "s")'.

     See also: butter.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Design lowpass analog Butterworth filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
butter


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1174
 -- Function File: [B, A] = butter (N, W)
 -- Function File: [B, A] = butter (N, W, "high")
 -- Function File: [B, A] = butter (N, [WL, WH])
 -- Function File: [B, A] = butter (N, [WL, WH], "stop")
 -- Function File: [Z, P, G] = butter (...)
 -- Function File: [A, B, C, D] = butter (...)
 -- Function File: [...] = butter (..., "s")
     Generate a Butterworth filter.  Default is a discrete space (Z)
     filter.

     [b,a] = butter(n, Wc) low pass filter with cutoff pi*Wc radians

     [b,a] = butter(n, Wc, 'high') high pass filter with cutoff pi*Wc
     radians

     [b,a] = butter(n, [Wl, Wh]) band pass filter with edges pi*Wl and
     pi*Wh radians

     [b,a] = butter(n, [Wl, Wh], 'stop') band reject filter with edges
     pi*Wl and pi*Wh radians

     [z,p,g] = butter(...)  return filter as zero-pole-gain rather than
     coefficients of the numerator and denominator polynomials.

     [...]  = butter(...,'s') return a Laplace space filter, W can be
     larger than 1.

     [a,b,c,d] = butter(...)  return state-space matrices

     References:

     Proakis & Manolakis (1992).  Digital Signal Processing.  New York:
     Macmillan Publishing Company.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
Generate a Butterworth filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
buttord


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1765
 -- Function File: N = buttord (WP, WS, RP, RS)
 -- Function File: N = buttord ([WP1, WP2], [WS1, WS2], RP, RS)
 -- Function File: [N, WC] = buttord (...)
     Compute the minimum filter order of a Butterworth filter with the
     desired response characteristics.  The filter frequency band edges
     are specified by the passband frequency WP and stopband frequency
     WS.  Frequencies are normalized to the Nyquist frequency in the
     range [0,1].  RP is the allowable passband ripple measured in
     decibels, and RS is the minimum attenuation in the stop band, also
     in decibels.  The output arguments N and WC can be given as inputs
     to 'butter'.

     If WP and WS are scalars, then WP is the passband cutoff frequency
     and WS is the stopband edge frequency.  If WS is greater than WP,
     the filter is a low-pass filter.  If WP is greater than WS, the
     filter is a high-pass filter.

     If WP and WS are vectors of length 2, then WP defines the passband
     interval and WS defines the stopband interval.  If WP is contained
     within WS (WS1 < WP1 < WP2 < WS2), the filter is a band-pass
     filter.  If WS is contained within WP (WP1 < WS1 < WS2 < WP2), the
     filter is a band-stop or band-reject filter.

     Theory: |H(W)|^2 = 1/[1+(W/Wc)^(2N)] = 10^(-R/10) With some
     algebra, you can solve simultaneously for Wc and N given Ws,Rs and
     Wp,Rp.  For high pass filters, subtracting the band edges from
     Fs/2, performing the test, and swapping the resulting Wc back works
     beautifully.  For bandpass and bandstop filters this process
     significantly overdesigns.  Artificially dividing N by 2 in this
     case helps a lot, but it still overdesigns.

     See also: butter, cheb1ord, cheb2ord, ellipord.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the minimum filter order of a Butterworth filter with the
desired respon



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
cceps


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 240
 -- Function File: cceps (X)
 -- Function File: cceps (X, CORRECT)
     Return the complex cepstrum of the vector X.  If the optional
     argument CORRECT has the value 1, a correction method is applied.
     The default is not to do this.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Return the complex cepstrum of the vector X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
cheb


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 428
 -- Function File: cheb (N, X)
     Returns the value of the nth-order Chebyshev polynomial calculated
     at the point x.  The Chebyshev polynomials are defined by the
     equations:

                    / cos(n acos(x),    |x| <= 1
            Tn(x) = |
                    \ cosh(n acosh(x),  |x| > 1

     If x is a vector, the output is a vector of the same size, where
     each element is calculated as y(i) = Tn(x(i)).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Returns the value of the nth-order Chebyshev polynomial calculated at
the point 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
cheb1ap


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 232
 -- Function File: [Z, P, G] = cheb1ap (N, RP)
     Design lowpass analog Chebyshev type I filter.

     This function exists for MATLAB compatibility only, and is
     equivalent to 'cheby1 (N, RP, 1, "s")'.

     See also: cheby1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Design lowpass analog Chebyshev type I filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
cheb1ord


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1308
 -- Function File: N = cheb1ord (WP, WS, RP, RS)
 -- Function File: N = cheb1ord ([WP1, WP2], [WS1, WS2], RP, RS)
 -- Function File: [N, WC] = cheb1ord (...)
     Compute the minimum filter order of a Chebyshev type I filter with
     the desired response characteristics.  The filter frequency band
     edges are specified by the passband frequency WP and stopband
     frequency WS.  Frequencies are normalized to the Nyquist frequency
     in the range [0,1].  RP is the allowable passband ripple measured
     in decibels, and RS is the minimum attenuation in the stop band,
     also in decibels.  The output arguments N and WC can be given as
     inputs to 'cheby1'.

     If WP and WS are scalars, then WP is the passband cutoff frequency
     and WS is the stopband edge frequency.  If WS is greater than WP,
     the filter is a low-pass filter.  If WP is greater than WS, the
     filter is a high-pass filter.

     If WP and WS are vectors of length 2, then WP defines the passband
     interval and WS defines the stopband interval.  If WP is contained
     within WS (WS1 < WP1 < WP2 < WS2), the filter is a band-pass
     filter.  If WS is contained within WP (WP1 < WS1 < WS2 < WP2), the
     filter is a band-stop or band-reject filter.

     See also: buttord, cheby1, cheb2ord, ellipord.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the minimum filter order of a Chebyshev type I filter with the
desired r



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
cheb2ap


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
 -- Function File: [Z, P, G] = cheb2ap (N, RS)
     Design lowpass analog Chebyshev type II filter.

     This function exists for MATLAB compatibility only, and is
     equivalent to 'cheby2 (N, RS, 1, "s")'.

     See also: cheby2.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Design lowpass analog Chebyshev type II filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
cheb2ord


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1309
 -- Function File: N = cheb2ord (WP, WS, RP, RS)
 -- Function File: N = cheb2ord ([WP1, WP2], [WS1, WS2], RP, RS)
 -- Function File: [N, WC] = cheb2ord (...)
     Compute the minimum filter order of a Chebyshev type II filter with
     the desired response characteristics.  The filter frequency band
     edges are specified by the passband frequency WP and stopband
     frequency WS.  Frequencies are normalized to the Nyquist frequency
     in the range [0,1].  RP is the allowable passband ripple measured
     in decibels, and RS is the minimum attenuation in the stop band,
     also in decibels.  The output arguments N and WC can be given as
     inputs to 'cheby2'.

     If WP and WS are scalars, then WP is the passband cutoff frequency
     and WS is the stopband edge frequency.  If WS is greater than WP,
     the filter is a low-pass filter.  If WP is greater than WS, the
     filter is a high-pass filter.

     If WP and WS are vectors of length 2, then WP defines the passband
     interval and WS defines the stopband interval.  If WP is contained
     within WS (WS1 < WP1 < WP2 < WS2), the filter is a band-pass
     filter.  If WS is contained within WP (WP1 < WS1 < WS2 < WP2), the
     filter is a band-stop or band-reject filter.

     See also: buttord, cheb1ord, cheby2, ellipord.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the minimum filter order of a Chebyshev type II filter with the
desired 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
chebwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1276
 -- Function File: chebwin (M)
 -- Function File: chebwin (M, AT)

     Return the filter coefficients of a Dolph-Chebyshev window of
     length M.  The Fourier transform of the window has a stop-band
     attenuation of AT dB. The default attenuation value is 100 dB.

     For the definition of the Chebyshev window, see

     * Peter Lynch, "The Dolph-Chebyshev Window: A Simple Optimal
     Filter", Monthly Weather Review, Vol.  125, pp.  655-660, April
     1997.  (http://www.maths.tcd.ie/~plynch/Publications/Dolph.pdf)

     * C. Dolph, "A current distribution for broadside arrays which
     optimizes the relationship between beam width and side-lobe level",
     Proc.  IEEE, 34, pp.  335-348.

     The window is described in frequency domain by the expression:

                   Cheb(m-1, beta * cos(pi * k/m))
            W(k) = -------------------------------
                          Cheb(m-1, beta)

     with

            beta = cosh(1/(m-1) * acosh(10^(at/20))

     and Cheb(m,x) denoting the m-th order Chebyshev polynomial
     calculated at the point x.

     Note that the denominator in W(k) above is not computed, and after
     the inverse Fourier transform the window is scaled by making its
     maximum value unitary.

     See also: kaiser.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 71
Return the filter coefficients of a Dolph-Chebyshev window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
cheby1


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1191
 -- Function File: [B, A] = cheby1 (N, RP, W)
 -- Function File: [B, A] = cheby1 (N, RP, W, "high")
 -- Function File: [B, A] = cheby1 (N, RP, [WL, WH])
 -- Function File: [B, A] = cheby1 (N, RP, [WL, WH], "stop")
 -- Function File: [Z, P, G] = cheby1 (...)
 -- Function File: [A, B, C, D] = cheby1 (...)
 -- Function File: [...] = cheby1 (..., "s")
     Generate a Chebyshev type I filter with RP dB of passband ripple.

     [b, a] = cheby1(n, Rp, Wc) low pass filter with cutoff pi*Wc
     radians

     [b, a] = cheby1(n, Rp, Wc, 'high') high pass filter with cutoff
     pi*Wc radians

     [b, a] = cheby1(n, Rp, [Wl, Wh]) band pass filter with edges pi*Wl
     and pi*Wh radians

     [b, a] = cheby1(n, Rp, [Wl, Wh], 'stop') band reject filter with
     edges pi*Wl and pi*Wh radians

     [z, p, g] = cheby1(...)  return filter as zero-pole-gain rather
     than coefficients of the numerator and denominator polynomials.

     [...]  = cheby1(...,'s') return a Laplace space filter, W can be
     larger than 1.

     [a,b,c,d] = cheby1(...)  return state-space matrices

     References:

     Parks & Burrus (1987).  Digital Filter Design.  New York: John
     Wiley & Sons, Inc.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Generate a Chebyshev type I filter with RP dB of passband ripple.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
cheby2


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1204
 -- Function File: [B, A] = cheby2 (N, RS, WC)
 -- Function File: [B, A] = cheby2 (N, RS, WC, "high")
 -- Function File: [B, A] = cheby2 (N, RS, [WL, WH])
 -- Function File: [B, A] = cheby2 (N, RS, [WL, WH], "stop")
 -- Function File: [Z, P, G] = cheby2 (...)
 -- Function File: [A, B, C, D] = cheby2 (...)
 -- Function File: [...] = cheby2 (..., "s")
     Generate a Chebyshev type II filter with RS dB of stopband
     attenuation.

     [b, a] = cheby2(n, Rs, Wc) low pass filter with cutoff pi*Wc
     radians

     [b, a] = cheby2(n, Rs, Wc, 'high') high pass filter with cutoff
     pi*Wc radians

     [b, a] = cheby2(n, Rs, [Wl, Wh]) band pass filter with edges pi*Wl
     and pi*Wh radians

     [b, a] = cheby2(n, Rs, [Wl, Wh], 'stop') band reject filter with
     edges pi*Wl and pi*Wh radians

     [z, p, g] = cheby2(...)  return filter as zero-pole-gain rather
     than coefficients of the numerator and denominator polynomials.

     [...]  = cheby2(...,'s') return a Laplace space filter, W can be
     larger than 1.

     [a,b,c,d] = cheby2(...)  return state-space matrices

     References:

     Parks & Burrus (1987).  Digital Filter Design.  New York: John
     Wiley & Sons, Inc.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 71
Generate a Chebyshev type II filter with RS dB of stopband attenuation.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
chirp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1084
 -- Function File: chirp (T)
 -- Function File: chirp (T, F0)
 -- Function File: chirp (T, F0, T1)
 -- Function File: chirp (T, F0, T1, F1)
 -- Function File: chirp (T, F0, T1, F1, FORM)
 -- Function File: chirp (T, F0, T1, F1, FORM, PHASE)

     Evaluate a chirp signal at time T.  A chirp signal is a frequency
     swept cosine wave.

     T
          vector of times to evaluate the chirp signal
     F0
          frequency at time t=0 [ 0 Hz ]
     T1
          time t1 [ 1 sec ]
     F1
          frequency at time t=t1 [ 100 Hz ]
     FORM
          shape of frequency sweep 'linear' f(t) = (f1-f0)*(t/t1) + f0
          'quadratic' f(t) = (f1-f0)*(t/t1)^2 + f0 'logarithmic' f(t) =
          (f1-f0)^(t/t1) + f0
     PHASE
          phase shift at t=0

     Example specgram(chirp([0:0.001:5])); # linear, 0-100Hz in 1 sec
     specgram(chirp([-2:0.001:15], 400, 10, 100, 'quadratic'));
     soundsc(chirp([0:1/8000:5], 200, 2, 500, "logarithmic"),8000);

     If you want a different sweep shape f(t), use the following: y =
     cos(2*pi*integral(f(t)) + 2*pi*f0*t + phase);


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
Evaluate a chirp signal at time T.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
clustersegment


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 710
 -- Function File: CLUSTERIDX = clustersegment (UNOS)
     Calculate boundary indexes of clusters of 1's.

     The function calculates the initial index and end index of the
     sequences of 1's in the rows of UNOS.  The clusters are sought in
     the rows of the array UNOS.

     The result is returned in a cell array of size 1-by-NP, where NP is
     the number of rows in UNOS.  Each element of the cell has two rows.
     The first row is the initial index of a sequence of 1's and the
     second row is the end index of that sequence.

     If NP == 1 the output is a matrix with two rows.

     The function works by finding the indexes of jumps between
     consecutive values in the rows of UNOS.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Calculate boundary indexes of clusters of 1's.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
cmorwavf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 99
 -- Function File: [PSI, X] = cmorwavf (LB, UB, N, FB, FC)
     Compute the Complex Morlet wavelet.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
Compute the Complex Morlet wavelet.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
cohere


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 377
 Usage:
   [Pxx,freq] = cohere(x,y,Nfft,Fs,window,overlap,range,plot_type,detrend)

     Estimate (mean square) coherence of signals "x" and "y".
     Use the Welch (1967) periodogram/FFT method.
     Compatible with Matlab R11 cohere and earlier.
     See "help pwelch" for description of arguments, hints and references
     --- especially hint (7) for Matlab R11 defaults.




# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
 Usage:
   [Pxx,freq] = cohere(x,y,Nfft,Fs,window,overlap,range,plot_type,detren



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
convmtx


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 494
 -- Function File: convmtx (A, N)
     If A is a column vector and X is a column vector of length N, then

     'convmtx(A, N) * X'

     gives the convolution of of A and X and is the same as 'conv(A,
     X)'.  The difference is if many vectors are to be convolved with
     the same vector, then this technique is possibly faster.

     Similarly, if A is a row vector and X is a row vector of length N,
     then

     'X * convmtx(A, N)'

     is the same as 'conv(X, A)'.

See also: conv.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
If A is a column vector and X is a column vector of length N, then



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
cplxreal


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 699
 -- Function File: [ZC, ZR] = cplxreal (Z, THRESH)
     Split the vector z into its complex (ZC) and real (ZR) elements,
     eliminating one of each complex-conjugate pair.

     INPUTS:
        * Z = row- or column-vector of complex numbers
        * THRESH = tolerance threshold for numerical comparisons
          (default = 100*eps)

     RETURNED:
        * ZC = elements of Z having positive imaginary parts
        * ZR = elements of Z having zero imaginary part

     Each complex element of Z is assumed to have a complex-conjugate
     counterpart elsewhere in Z as well.  Elements are declared real if
     their imaginary parts have magnitude less than THRESH.

     See also: cplxpair.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Split the vector z into its complex (ZC) and real (ZR) elements,
eliminating one



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
cpsd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 503
 -- Function File: [PXX, FREQ] = cpsd (X, Y)
 -- Function File: [...] = cpsd (X, Y, WINDOW)
 -- Function File: [...] = cpsd (X, Y, WINDOW, OVERLAP)
 -- Function File: [...] = cpsd (X, Y, WINDOW, OVERLAP, NFFT)
 -- Function File: [...] = cpsd (X, Y, WINDOW, OVERLAP, NFFT, FS)
 -- Function File: [...] = cpsd (X, Y, WINDOW, OVERLAP, NFFT, FS, RANGE)
 -- Function File: cpsd (...)

     Estimate cross power spectrum of data X and Y by the Welch (1967)
     periodogram/FFT method.

     See also: pwelch.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Estimate cross power spectrum of data X and Y by the Welch (1967)
periodogram/FF



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
csd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 358
 Usage:
   [Pxx,freq] = csd(x,y,Nfft,Fs,window,overlap,range,plot_type,detrend)

     Estimate cross power spectrum of data "x" and "y" by the Welch (1967)
     periodogram/FFT method.  Compatible with Matlab R11 csd and earlier.
     See "help pwelch" for description of arguments, hints and references
     --- especially hint (7) for Matlab R11 defaults.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 79
 Usage:
   [Pxx,freq] = csd(x,y,Nfft,Fs,window,overlap,range,plot_type,detrend)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
czt


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 978
 -- Function File: czt (X)
 -- Function File: czt (X, M)
 -- Function File: czt (X, M, W)
 -- Function File: czt (X, M, W, A)
     Chirp z-transform.  Compute the frequency response starting at a
     and stepping by w for m steps.  a is a point in the complex plane,
     and w is the ratio between points in each step (i.e., radius
     increases exponentially, and angle increases linearly).

     To evaluate the frequency response for the range f1 to f2 in a
     signal with sampling frequency Fs, use the following:

          m = 32;                               ## number of points desired
          w = exp(-j*2*pi*(f2-f1)/((m-1)*Fs));  ## freq. step of f2-f1/m
          a = exp(j*2*pi*f1/Fs);                ## starting at frequency f1
          y = czt(x, m, w, a);

     If you don't specify them, then the parameters default to a Fourier
     transform: m=length(x), w=exp(-j*2*pi/m), a=1

     If x is a matrix, the transform will be performed column-by-column.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Chirp z-transform.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
data2fun


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1111
 -- Function File: [FHANDLE, FULLNAME] = data2fun (TI, YI)
 -- Function File: [...] = data2fun (TI, YI,PROPERTY,VALUE)
     Creates a vectorized function based on data samples using
     interpolation.

     The values given in YI (N-by-k matrix) correspond to evaluations of
     the function y(t) at the points TI (N-by-1 matrix).  The data is
     interpolated and the function handle to the generated interpolant
     is returned.

     The function accepts property-value pairs described below.

     'file'
          Code is generated and .m file is created.  The VALUE contains
          the name of the function.  The returned function handle is a
          handle to that file.  If VALUE is empty, then a name is
          automatically generated using 'tmpnam' and the file is created
          in the current directory.  VALUE must not have an extension,
          since .m will be appended.  Numerical value used in the
          function are stored in a .mat file with the same name as the
          function.

     'interp'
          Type of interpolation.  See 'interp1'.

     See also: interp1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
Creates a vectorized function based on data samples using interpolation.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
dct


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 779
 -- Function File: dct (X)
 -- Function File: dct (X, N)
     Compute the discrete cosine transform of X.  If N is given, then X
     is padded or trimmed to length N before computing the transform.
     If X is a matrix, compute the transform along the columns of the
     the matrix.  The transform is faster if X is real-valued and has
     even length.

     The discrete cosine transform X can be defined as follows:

                        N-1
            X[k] = w(k) sum x[n] cos (pi (2n+1) k / 2N ),  k = 0, ..., N-1
                        n=0

     with w(0) = sqrt(1/N) and w(k) = sqrt(2/N), k = 1, ..., N-1.  There
     are other definitions with different scaling of X[k], but this form
     is common in image processing.

     See also: idct, dct2, idct2, dctmtx.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Compute the discrete cosine transform of X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
dct2


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 275
 -- Function File: dct2 (X)
 -- Function File: dct2 (X, M, N)
 -- Function File: dct2 (X, [M, N])
     Compute the 2-D discrete cosine transform of matrix X.  If M and N
     are specified, the input is padded or trimmed to the desired size.

     See also: dct, idct, idct2.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
Compute the 2-D discrete cosine transform of matrix X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
dctmtx


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 670
 -- Function File: dctmtx (N)
     Return the DCT transformation matrix of size N-by-N.

     If A is an N-by-N matrix, then the following are true:

              T*A    == dct(A),  T'*A   == idct(A)
              T*A*T' == dct2(A), T'*A*T == idct2(A)

     A DCT transformation matrix is useful for doing things like jpeg
     image compression, in which an 8x8 DCT matrix is applied to
     non-overlapping blocks throughout an image and only a subblock on
     the top left of each block is kept.  During restoration, the
     remainder of the block is filled with zeros and the inverse
     transform is applied to the block.

     See also: dct, idct, dct2, idct2.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Return the DCT transformation matrix of size N-by-N.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
decimate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1381
 -- Function File: Y = decimate (X, Q)
 -- Function File: Y = decimate (X, Q, N)
 -- Function File: Y = decimate (..., "fir")

     Downsample the signal X by a reduction factor of Q.  A lowpass
     antialiasing filter is applied to the signal prior to reducing the
     input sequence.  By default, an order N Chebyshev type I filter is
     used.  If N is not specified, the default is 8.

     If the optional argument '"fir"' is given, an order N FIR filter is
     used, with a default order of 30 if N is not given.

     Note that Q must be an integer for this rate change method.

     Example:
          ## Generate a signal that starts away from zero, is slowly varying
          ## at the start and quickly varying at the end, decimate and plot.
          ## Since it starts away from zero, you will see the boundary
          ## effects of the antialiasing filter clearly.  Next you will see
          ## how it follows the curve nicely in the slowly varying early
          ## part of the signal, but averages the curve in the quickly
          ## varying late part of the signal.
          t = 0:0.01:2;
          x = chirp (t, 2, .5, 10, "quadratic") + sin (2*pi*t*0.4);
          y = decimate (x, 4);
          stem (t(1:121) * 1000, x(1:121), "-g;Original;"); hold on; # original
          stem (t(1:4:121) * 1000, y(1:31), "-r;Decimated;"); hold off; # decimated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Downsample the signal X by a reduction factor of Q.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
dftmtx


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 410
 -- Function File: D = dftmtx (N)
     Compute the N-by-N Fourier transformation matrix.  This is the
     matrix D such that the Fourier transform of a column vector of
     length N is given by 'dftmtx(N) * X' and the inverse Fourier
     transform is given by 'inv(dftmtx(N)) * X'.

     In general this is less efficient than calling the 'fft' and 'ifft'
     functions directly.

     See also: fft, ifft.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the N-by-N Fourier transformation matrix.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
digitrevorder


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 330
 -- Function File: Y = digitrevorder (X, R)
 -- Function File: [Y, I] = digitrevorder (X, R)
     Reorder the elements of the vector X in digit-reversed order.  The
     elements of X are converted to radix R and reversed.  The reordered
     indices of the elements of X are returned in I.

     See also: bitrevorder, fft, ifft.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Reorder the elements of the vector X in digit-reversed order.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
diric


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 113
 -- Function File: Y = diric (X,N)
     Compute the dirichlet function.

     See also: sinc, gauspuls, sawtooth.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
Compute the dirichlet function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
downsample


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 509
 -- Function File: Y = downsample (X, N)
 -- Function File: Y = downsample (X, N, OFFSET)
     Downsample the signal, selecting every Nth element.  If X is a
     matrix, downsample every column.

     For most signals you will want to use 'decimate' instead since it
     prefilters the high frequency components of the signal and avoids
     aliasing effects.

     If OFFSET is defined, select every Nth element starting at sample
     OFFSET.

     See also: decimate, interp, resample, upfirdn, upsample.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Downsample the signal, selecting every Nth element.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
dst


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 480
 -- Function File: Y = dst (X)
 -- Function File: Y = dst (X, N)
     Computes the type I discrete sine transform of X.  If N is given,
     then X is padded or trimmed to length N before computing the
     transform.  If X is a matrix, compute the transform along the
     columns of the the matrix.

     The discrete sine transform X of x can be defined as follows:

            N
     X[k] = sum x[n] sin (pi n k / (N+1) ),  k = 1, ..., N
            n=1

     See also: idst.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Computes the type I discrete sine transform of X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
dwt


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 522
 -- Function File: [U, V] = dwt (X, WNAME)
 -- Function File: [U, V] = dwt (X, HP, GP)
 -- Function File: [U, V] = dwt (X, HP, GP, ...)
     Discrete wavelet transform (1D).

     *Inputs*
     X
          Signal vector.
     WNAME
          Wavelet name.
     HP
          Coefficients of low-pass decomposition FIR filter.
     GP
          Coefficients of high-pass decomposition FIR filter.

     *Outputs*
     U
          Signal vector of average, approximation.
     V
          Signal vector of difference, detail.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
Discrete wavelet transform (1D).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
ellip


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1442
 -- Function File: [B, A] = ellip (N, RP, RS, WP)
 -- Function File: [B, A] = ellip (N, RP, RS, WP, "high")
 -- Function File: [B, A] = ellip (N, RP, RS, [WL, WH])
 -- Function File: [B, A] = ellip (N, RP, RS, [WL, WH], "stop")
 -- Function File: [Z, P, G] = ellip (...)
 -- Function File: [A, B, C, D] = ellip (...)
 -- Function File: [...] = ellip (..., "s")

     Generate an elliptic or Cauer filter with RP dB of passband ripple
     and RS dB of stopband attenuation.

     [b,a] = ellip(n, Rp, Rs, Wp) low pass filter with order n, cutoff
     pi*Wp radians, Rp decibels of ripple in the passband and a stopband
     Rs decibels down.

     [b,a] = ellip(n, Rp, Rs, Wp, 'high') high pass filter with cutoff
     pi*Wp...

     [b,a] = ellip(n, Rp, Rs, [Wl, Wh]) band pass filter with band pass
     edges pi*Wl and pi*Wh ...

     [b,a] = ellip(n, Rp, Rs, [Wl, Wh], 'stop') band reject filter with
     edges pi*Wl and pi*Wh, ...

     [z,p,g] = ellip(...)  return filter as zero-pole-gain.

     [...]  = ellip(...,'s') return a Laplace space filter, W can be
     larger than 1.

     [a,b,c,d] = ellip(...)  return state-space matrices

     References:

     - Oppenheim, Alan V., Discrete Time Signal Processing, Hardcover,
     1999.  - Parente Ribeiro, E., Notas de aula da disciplina TE498 -
     Processamento Digital de Sinais, UFPR, 2001/2002.  - Kienzle, Paul,
     functions from Octave-Forge, 1999 (http://octave.sf.net).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Generate an elliptic or Cauer filter with RP dB of passband ripple and
RS dB of 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
ellipap


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 230
 -- Function File: [Z, P, G] = ellipap (N, RP, RS)
     Design lowpass analog elliptic filter.

     This function exists for MATLAB compatibility only, and is
     equivalent to 'ellip (N, RP, RS, 1, "s")'.

     See also: ellip.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Design lowpass analog elliptic filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
ellipord


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1426
 -- Function File: N = ellipord (WP, WS, RP, RS)
 -- Function File: N = ellipord ([WP1, WP2], [WS1, WS2], RP, RS)
 -- Function File: [N, WC] = ellipord (...)
     Compute the minimum filter order of an elliptic filter with the
     desired response characteristics.  The filter frequency band edges
     are specified by the passband frequency WP and stopband frequency
     WS.  Frequencies are normalized to the Nyquist frequency in the
     range [0,1].  RP is the allowable passband ripple measured in
     decibels, and RS is the minimum attenuation in the stop band, also
     in decibels.  The output arguments N and WC can be given as inputs
     to 'ellip'.

     If WP and WS are scalars, then WP is the passband cutoff frequency
     and WS is the stopband edge frequency.  If WS is greater than WP,
     the filter is a low-pass filter.  If WP is greater than WS, the
     filter is a high-pass filter.

     If WP and WS are vectors of length 2, then WP defines the passband
     interval and WS defines the stopband interval.  If WP is contained
     within WS (WS1 < WP1 < WP2 < WS2), the filter is a band-pass
     filter.  If WS is contained within WP (WP1 < WS1 < WS2 < WP2), the
     filter is a band-stop or band-reject filter.

     Reference: Lamar, Marcus Vinicius, 'Notas de aula da disciplina TE
     456 - Circuitos Analogicos II', UFPR, 2001/2002.

     See also: buttord, cheb1ord, cheb2ord, ellip.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the minimum filter order of an elliptic filter with the desired
response



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
fht


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 776
 -- Function File: M = fht (D)
 -- Function File: M = fht (D, N)
 -- Function File: M = fht (D, N, DIM)
     Calculate the Fast Hartley Transform of real input D.  If D is a
     matrix, the Hartley transform is calculated along the columns by
     default.  The options N and DIM are similar to the options of FFT
     function.

     The forward and inverse Hartley transforms are the same (except for
     a scale factor of 1/N for the inverse Hartley transform), but
     implemented using different functions.

     The definition of the forward hartley transform for vector d, m[K]
     = \sum_{i=0}^{N-1} d[i]*(cos[K*2*pi*i/N] + sin[K*2*pi*i/N]), for 0
     <= K < N. m[K] = \sum_{i=0}^{N-1} d[i]*CAS[K*i], for 0 <= K < N.

          fht(1:4)

     See also: ifht, fft.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
Calculate the Fast Hartley Transform of real input D.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
filtfilt


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 737
 -- Function File: Y = filtfilt (B, A, X)

     Forward and reverse filter the signal.  This corrects for phase
     distortion introduced by a one-pass filter, though it does square
     the magnitude response in the process.  That's the theory at least.
     In practice the phase correction is not perfect, and magnitude
     response is distorted, particularly in the stop band.

     Example
          [b, a]=butter(3, 0.1);                  # 5 Hz low-pass filter
          t = 0:0.01:1.0;                         # 1 second sample
          x=sin(2*pi*t*2.3)+0.25*randn(size(t));  # 2.3 Hz sinusoid+noise
          y = filtfilt(b,a,x); z = filter(b,a,x); # apply filter
          plot(t,x,';data;',t,y,';filtfilt;',t,z,';filter;')


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Forward and reverse filter the signal.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
filtic


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 847
 -- Function File: ZF = filtic (B, A, Y)
 -- Function File: ZF = filtic (B, A, Y, X)

     Set initial condition vector for filter function The vector zf has
     the same values that would be obtained from function filter given
     past inputs x and outputs y

     The vectors x and y contain the most recent inputs and outputs
     respectively, with the newest values first:

     x = [x(-1) x(-2) ...  x(-nb)], nb = length(b)-1 y = [y(-1) y(-2)
     ...  y(-na)], na = length(a)-a

     If length(x)<nb then it is zero padded If length(y)<na then it is
     zero padded

     zf = filtic(b, a, y) Initial conditions for filter with
     coefficients a and b and output vector y, assuming input vector x
     is zero

     zf = filtic(b, a, y, x) Initial conditions for filter with
     coefficients a and b input vector x and output vector y


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Set initial condition vector for filter function The vector zf has the
same valu



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
findpeaks


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2797
 -- Function File: [PKS, LOC, EXTRA] = findpeaks (DATA)
 -- Function File: ... = findpeaks (..., PROPERTY, VALUE)
 -- Function File: ... = findpeaks (..., "DoubleSided")
     Finds peaks on DATA.

     Peaks of a positive array of data are defined as local maxima.  For
     double-sided data, they are maxima of the positive part and minima
     of the negative part.  DATA is expected to be a single column
     vector.

     The function returns the value of DATA at the peaks in PKS.  The
     index indicating their position is returned in LOC.

     The third output argument is a structure with additional
     information:

     "parabol"
          A structure containing the parabola fitted to each returned
          peak.  The structure has two fields, "x" and "pp".  The field
          "pp" contains the coefficients of the 2nd degree polynomial
          and "x" the extrema of the intercal here it was fitted.

     "height"
          The estimated height of the returned peaks (in units of DATA).

     "baseline"
          The height at which the roots of the returned peaks were
          calculated (in units of DATA).

     "roots"
          The abscissa values (in index units) at which the parabola
          fitted to each of the returned peaks crosses the "baseline"
          value.  The width of the peak is calculated by 'diff(roots)'.

     This function accepts property-value pair given in the list below:

     "MinPeakHeight"
          Minimum peak height (positive scalar).  Only peaks that exceed
          this value will be returned.  For data taking positive and
          negative values use the option "DoubleSided".  Default value
          '2*std (abs (detrend (data,0)))'.

     "MinPeakDistance"
          Minimum separation between (positive integer).  Peaks
          separated by less than this distance are considered a single
          peak.  This distance is also used to fit a second order
          polynomial to the peaks to estimate their width, therefore it
          acts as a smoothing parameter.  Default value 4.

     "MinPeakWidth"
          Minimum width of peaks (positive integer).  The width of the
          peaks is estimated using a parabola fitted to the neighborhood
          of each peak.  The neighborhood size is equal to the value of
          "MinPeakDistance".  The width is evaluated at the half height
          of the peak with baseline at "MinPeakHeight".  Default value
          2.

     "DoubleSided"
          Tells the function that data takes positive and negative
          values.  The base-line for the peaks is taken as the mean
          value of the function.  This is equivalent as passing the
          absolute value of the data after removing the mean.

     Run 'demo findpeaks' to see some examples.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Finds peaks on DATA.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
fir1


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1553
 -- Function File: B = fir1 (N, W)
 -- Function File: B = fir1 (N, W, TYPE)
 -- Function File: B = fir1 (N, W, TYPE, WINDOW)
 -- Function File: B = fir1 (N, W, TYPE, WINDOW, NOSCALE)

     Produce an order N FIR filter with the given frequency cutoff W,
     returning the N+1 filter coefficients in B.  If W is a scalar, it
     specifies the frequency cutoff for a lowpass or highpass filter.
     If W is a two-element vector, the two values specify the edges of a
     bandpass or bandstop filter.  If W is an N-element vector, each
     value specifies a band edge of a multiband pass/stop filter.

     The filter TYPE can be specified with one of the following strings:
     "low", "high", "stop", "pass", "bandpass", "DC-0", or "DC-1".  The
     default is "low" is W is a scalar, "pass" if W is a pair, or "DC-0"
     if W is a vector with more than 2 elements.

     An optional shaping WINDOW can be given as a vector with length
     N+1.  If not specified, a Hamming window of length N+1 is used.

     With the option "noscale", the filter coefficients are not
     normalized.  The default is to normalize the filter such that the
     magnitude response of the center of the first passband is 1.

     To apply the filter, use the return vector B with the 'filter'
     function, for example 'y = filter (b, 1, x)'.

     Examples:
          freqz (fir1 (40, 0.3));
          freqz (fir1 (15, [0.2, 0.5], "stop"));  # note the zero-crossing at 0.1
          freqz (fir1 (15, [0.2, 0.5], "stop", "noscale"));

     See also: filter, fir2.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Produce an order N FIR filter with the given frequency cutoff W,
returning the N



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
fir2


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1672
 -- Function File: B = fir2 (N, F, M)
 -- Function File: B = fir2 (N, F, M, GRID_N)
 -- Function File: B = fir2 (N, F, M, GRID_N, RAMP_N)
 -- Function File: B = fir2 (N, F, M, GRID_N, RAMP_N, WINDOW)

     Produce an order N FIR filter with arbitrary frequency response M
     over frequency bands F, returning the N+1 filter coefficients in B.
     The vector F specifies the frequency band edges of the filter
     response and M specifies the magnitude response at each frequency.

     The vector F must be nondecreasing over the range [0,1], and the
     first and last elements must be 0 and 1, respectively.  A
     discontinuous jump in the frequency response can be specified by
     duplicating a band edge in F with different values in M.

     The resolution over which the frequency response is evaluated can
     be controlled with the GRID_N argument.  The default is 512 or the
     next larger power of 2 greater than the filter length.

     The band transition width for discontinuities can be controlled
     with the RAMP_N argument.  The default is GRID_N/25.  Larger values
     will result in wider band transitions but better stopband
     rejection.

     An optional shaping WINDOW can be given as a vector with length
     N+1.  If not specified, a Hamming window of length N+1 is used.

     To apply the filter, use the return vector B with the 'filter'
     function, for example 'y = filter (b, 1, x)'.

     Example:
          f = [0, 0.3, 0.3, 0.6, 0.6, 1]; m = [0, 0, 1, 1/2, 0, 0];
          [h, w] = freqz (fir2 (100, f, m));
          plot (f, m, ";target response;", w/pi, abs (h), ";filter response;");

     See also: filter, fir1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Produce an order N FIR filter with arbitrary frequency response M over
frequency



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
firls


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1113
 -- Function File: B = firls (N, F, A)
 -- Function File: B = firls (N, F, A, W)

     FIR filter design using least squares method.  Returns a length N+1
     linear phase filter such that the integral of the weighted mean
     squared error in the specified bands is minimized.

     The vector F specifies the frequencies of the band edges,
     normalized so that half the sample frequency is equal to 1.  Each
     band is specified by two frequencies, to the vector must have an
     even length.

     The vector A specifies the amplitude of the desired response at
     each band edge.

     The optional argument W is a weighting function that contains one
     value for each band that weights the mean squared error in that
     band.

     A must be the same length as F, and W must be half the length of F.
     N must be even.  If given an odd value, 'firls' increments it by 1.

     The least squares optimization algorithm for computing FIR filter
     coefficients is derived in detail in:

     I. Selesnick, "Linear-Phase FIR Filter Design by Least Squares,"
     http://cnx.org/content/m10577


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
FIR filter design using least squares method.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
flattopwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 918
 -- Function File: flattopwin (M)
 -- Function File: flattopwin (M, "periodic")
 -- Function File: flattopwin (M, "symmetric")

     Return the filter coefficients of a Flat Top window of length M.
     The Flat Top window is defined by the function f(w):

            f(w) = 1 - 1.93 cos(2 pi w) + 1.29 cos(4 pi w)
                     - 0.388 cos(6 pi w) + 0.0322cos(8 pi w)

     where w = i/(m-1) for i=0:m-1 for a symmetric window, or w = i/m
     for i=0:m-1 for a periodic window.  The default is symmetric.  The
     returned window is normalized to a peak of 1 at w = 0.5.

     This window has low pass-band ripple, but high bandwidth.

     According to [1]:

     The main use for the Flat Top window is for calibration, due to its
     negligible amplitude errors.

     [1] Gade, S; Herlufsen, H; (1987) "Use of weighting functions in
     DFT/FFT analysis (Part I)", Bruel & Kjaer Technical Review No.3.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Return the filter coefficients of a Flat Top window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
fracshift


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
 -- Function File: [Y, H] = fracshift (X, D)
 -- Function File: Y = fracshift (X, D, H)
     Shift the series X by a (possibly fractional) number of samples D.
     The interpolator H is either specified or either designed with a
     Kaiser-windowed sinecard.

     See also: circshift.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Shift the series X by a (possibly fractional) number of samples D.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
freqs


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 385
 -- Function File: H = freqs (B, A, W)
 -- Function File: freqs (B, A, W)

     Compute the s-plane frequency response of the IIR filter B(s)/A(s)
     as H = polyval(B,j*W)./polyval(A,j*W). If called with no output
     argument, a plot of magnitude and phase are displayed.

     Example:
          b = [1 2]; a = [1 1];
          w = linspace (0, 4, 128);
          freqs (b, a, w);


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the s-plane frequency response of the IIR filter B(s)/A(s) as H
= polyva



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
freqs_plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 87
 -- Function File: freqs_plot (W, H)
     Plot the amplitude and phase of the vector H.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
Plot the amplitude and phase of the vector H.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
fwhm


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1264
 -- Function File: F = fwhm (Y)
 -- Function File: F = fwhm (X, Y)
 -- Function File: F = fwhm (..., "zero")
 -- Function File: F = fwhm (..., "min")
 -- Function File: F = fwhm (..., "alevel", LEVEL)
 -- Function File: F = fwhm (..., "rlevel", LEVEL)

     Compute peak full-width at half maximum (FWHM) or at another level
     of peak maximum for vector or matrix data Y, optionally sampled as
     y(x).  If Y is a matrix, return FWHM for each column as a row
     vector.

     The default option "zero" computes fwhm at half maximum, i.e.
     0.5*max(y).  The option "min" computes fwhm at the middle curve,
     i.e.  0.5*(min(y)+max(y)).

     The option "rlevel" computes full-width at the given relative level
     of peak profile, i.e.  at rlevel*max(y) or rlevel*(min(y)+max(y)),
     respectively.  For example, 'fwhm (..., "rlevel", 0.1)' computes
     full width at 10 % of peak maximum with respect to zero or minimum;
     FWHM is equivalent to 'fwhm(..., "rlevel", 0.5)'.

     The option "alevel" computes full-width at the given absolute level
     of Y.

     Return 0 if FWHM does not exist (e.g.  monotonous function or the
     function does not cut horizontal line at rlevel*max(y) or
     rlevel*(max(y)+min(y)) or alevel, respectively).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute peak full-width at half maximum (FWHM) or at another level of
peak maxim



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
fwht


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 981
 -- Function File: fwht (X)
 -- Function File: fwht (X, N)
 -- Function File: fwht (X, N, ORDER)
     Compute the Walsh-Hadamard transform of X using the Fast
     Walsh-Hadamard Transform (FWHT) algorithm.  If the input is a
     matrix, the FWHT is calculated along the columns of X.

     The number of elements of X must be a power of 2; if not, the input
     will be extended and filled with zeros.  If a second argument is
     given, the input is truncated or extended to have length N.

     The third argument specifies the ORDER in which the returned
     Walsh-Hadamard transform coefficients should be arranged.  The
     ORDER may be any of the following strings:

     "sequency"
          The coefficients are returned in sequency order.  This is the
          default if ORDER is not given.

     "hadamard"
          The coefficients are returned in Hadamard order.

     "dyadic"
          The coefficients are returned in Gray code order.

     See also: ifwht.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the Walsh-Hadamard transform of X using the Fast Walsh-Hadamard
Transfor



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
gauspuls


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 94
 -- Function File: Y = gauspuls (T,FC,BW)
     Return the Gaussian modulated sinusoidal pulse.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Return the Gaussian modulated sinusoidal pulse.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
gaussian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 560
 -- Function File: gaussian (M)
 -- Function File: gaussian (M, A)

     Return a Gaussian convolution window of length M.  The width of the
     window is inversely proportional to the parameter A.  Use larger A
     for a narrower window.  Use larger M for longer tails.

     w = exp ( -(a*x)^2/2 )

     for x = linspace ( -(m-1)/2, (m-1)/2, m ).

     Width a is measured in frequency units (sample rate/num samples).
     It should be f when multiplying in the time domain, but 1/f when
     multiplying in the frequency domain (for use in convolutions).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Return a Gaussian convolution window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
gausswin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 367
 -- Function File: gausswin (M)
 -- Function File: gausswin (M, A)

     Return the filter coefficients of a Gaussian window of length M.
     The width of the window is inversely proportional to the parameter
     A.  Use larger A for a narrow window.  Use larger M for a smoother
     curve.

     w = exp ( -(a*x)^2/2 )

     for x = linspace(-(m-1)/m, (m-1)/m, m)


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Return the filter coefficients of a Gaussian window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
gmonopuls


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 75
 -- Function File: Y = gmonopuls (T,FC)
     Return the gaussian monopulse.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
Return the gaussian monopulse.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
grpdelay


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3129
 -- Function File: [G, W] = grpdelay (B)
 -- Function File: [G, W] = grpdelay (B, A)
 -- Function File: [G, W] = grpdelay (..., N)
 -- Function File: [G, W] = grpdelay (..., N, "whole")
 -- Function File: [G, F] = grpdelay (..., N, FS)
 -- Function File: [G, F] = grpdelay (..., N, "whole", FS)
 -- Function File: [G, W] = grpdelay (..., W)
 -- Function File: [G, F] = grpdelay (..., F, FS)
 -- Function File: grpdelay (...)
     Compute the group delay of a filter.

     [g, w] = grpdelay(b) returns the group delay g of the FIR filter
     with coefficients b.  The response is evaluated at 512 angular
     frequencies between 0 and pi.  w is a vector containing the 512
     frequencies.  The group delay is in units of samples.  It can be
     converted to seconds by multiplying by the sampling period (or
     dividing by the sampling rate fs).

     [g, w] = grpdelay(b,a) returns the group delay of the rational IIR
     filter whose numerator has coefficients b and denominator
     coefficients a.

     [g, w] = grpdelay(b,a,n) returns the group delay evaluated at n
     angular frequencies.  For fastest computation n should factor into
     a small number of small primes.

     [g, w] = grpdelay(b,a,n,'whole') evaluates the group delay at n
     frequencies between 0 and 2*pi.

     [g, f] = grpdelay(b,a,n,Fs) evaluates the group delay at n
     frequencies between 0 and Fs/2.

     [g, f] = grpdelay(b,a,n,'whole',Fs) evaluates the group delay at n
     frequencies between 0 and Fs.

     [g, w] = grpdelay(b,a,w) evaluates the group delay at frequencies w
     (radians per sample).

     [g, f] = grpdelay(b,a,f,Fs) evaluates the group delay at
     frequencies f (in Hz).

     grpdelay(...)  plots the group delay vs.  frequency.

     If the denominator of the computation becomes too small, the group
     delay is set to zero.  (The group delay approaches infinity when
     there are poles or zeros very close to the unit circle in the z
     plane.)

     Theory: group delay, g(w) = -d/dw [arg{H(e^jw)}], is the rate of
     change of phase with respect to frequency.  It can be computed as:

                        d/dw H(e^-jw)
                 g(w) = -------------
                          H(e^-jw)

     where

                  H(z) = B(z)/A(z) = sum(b_k z^k)/sum(a_k z^k).

     By the quotient rule,

                             A(z) d/dw B(z) - B(z) d/dw A(z)
                 d/dw H(z) = -------------------------------
                                        A(z) A(z)

     Substituting into the expression above yields:

                         A dB - B dA
                 g(w) =  ----------- = dB/B - dA/A
                             A B

     Note that,

                 d/dw B(e^-jw) = sum(k b_k e^-jwk)
                 d/dw A(e^-jw) = sum(k a_k e^-jwk)

     which is just the FFT of the coefficients multiplied by a ramp.

     As a further optimization when nfft>>length(a), the IIR filter
     (b,a) is converted to the FIR filter conv(b,fliplr(conj(a))).  For
     further details, see
     http://ccrma.stanford.edu/~jos/filters/Numerical_Computation_Group_Delay.html


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Compute the group delay of a filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
hann


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 591
 -- Function File: hann (M)
 -- Function File: hann (M, "periodic")
 -- Function File: hann (M, "symmetric")
     Return the filter coefficients of a Hanning window of length M.

     If the optional argument '"periodic"' is given, the periodic form
     of the window is returned.  This is equivalent to the window of
     length M+1 with the last coefficient removed.  The optional
     argument '"symmetric"' is equivalent to not specifying a second
     argument.

     This function exists for MATLAB compatibility only, and is
     equivalent to 'hanning (M)'.

     See also: hanning.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 63
Return the filter coefficients of a Hanning window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
hilbert


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 663
 -- Function File: H = hilbert (F, N, DIM)
     Analytic extension of real valued signal.

     'H = hilbert (F)' computes the extension of the real valued signal
     F to an analytic signal.  If F is a matrix, the transformation is
     applied to each column.  For N-D arrays, the transformation is
     applied to the first non-singleton dimension.

     'real (H)' contains the original signal F.  'imag (H)' contains the
     Hilbert transform of F.

     'hilbert (F, N)' does the same using a length N Hilbert transform.
     The result will also have length N.

     'hilbert (F, [], DIM)' or 'hilbert (F, N, DIM)' does the same along
     dimension DIM.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Analytic extension of real valued signal.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
idct


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 674
 -- Function File: Y = idct (X)
 -- Function File: Y = idct (X, N)
     Compute the inverse discrete cosine transform of X.  If N is given,
     then X is padded or trimmed to length N before computing the
     transform.  If X is a matrix, compute the transform along the
     columns of the the matrix.  The transform is faster if X is
     real-valued and even length.

     The inverse discrete cosine transform X can be defined as follows:

                   N-1
            x[n] = sum w(k) X[k] cos (pi (2n+1) k / 2N ),  n = 0, ..., N-1
                   k=0

     with w(0) = sqrt(1/N) and w(k) = sqrt(2/N), k = 1, ..., N-1

     See also: dct, dct2, idct2, dctmtx.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the inverse discrete cosine transform of X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
idct2


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
 -- Function File: Y = idct2 (X)
 -- Function File: Y = idct2 (X, M, N)
 -- Function File: Y = idct2 (X, [M, N])
     Compute the inverse 2-D discrete cosine transform of matrix X.  If
     M and N are specified, the input is either padded or truncated to
     have M rows and N columns.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the inverse 2-D discrete cosine transform of matrix X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
idst


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 331
 -- Function File: Y = idst (X)
 -- Function File: Y = idst (X, N)
     Computes the inverse type I discrete sine transform of Y.  If N is
     given, then Y is padded or trimmed to length N before computing the
     transform.  If Y is a matrix, compute the transform along the
     columns of the the matrix.

     See also: dst.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
Computes the inverse type I discrete sine transform of Y.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
ifht


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 741
 -- Function File: M = ifht (D, N, DIM)
     Calculate the inverse Fast Hartley Transform of real input D.  If D
     is a matrix, the inverse Hartley transform is calculated along the
     columns by default.  The options N and DIM are similar to the
     options of FFT function.

     The forward and inverse Hartley transforms are the same (except for
     a scale factor of 1/N for the inverse hartley transform), but
     implemented using different functions.

     The definition of the forward hartley transform for vector d, m[K]
     = 1/N \sum_{i=0}^{N-1} d[i]*(cos[K*2*pi*i/N] + sin[K*2*pi*i/N]),
     for 0 <= K < N. m[K] = 1/N \sum_{i=0}^{N-1} d[i]*CAS[K*i], for 0 <=
     K < N.

          ifht(1:4)

     See also: fht, fft.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Calculate the inverse Fast Hartley Transform of real input D.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
ifwht


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1006
 -- Function File: ifwht (X)
 -- Function File: ifwht (X, N)
 -- Function File: ifwht (X, N, ORDER)
     Compute the inverse Walsh-Hadamard transform of X using the Fast
     Walsh-Hadamard Transform (FWHT) algorithm.  If the input is a
     matrix, the inverse FWHT is calculated along the columns of X.

     The number of elements of X must be a power of 2; if not, the input
     will be extended and filled with zeros.  If a second argument is
     given, the input is truncated or extended to have length N.

     The third argument specifies the ORDER in which the returned
     inverse Walsh-Hadamard transform coefficients should be arranged.
     The ORDER may be any of the following strings:

     "sequency"
          The coefficients are returned in sequency order.  This is the
          default if ORDER is not given.

     "hadamard"
          The coefficients are returned in Hadamard order.

     "dyadic"
          The coefficients are returned in Gray code order.

     See also: fwht.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the inverse Walsh-Hadamard transform of X using the Fast
Walsh-Hadamard 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
iirlp2mb


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1305
 IIR Low Pass Filter to Multiband Filter Transformation

 [Num,Den,AllpassNum,AllpassDen] = iirlp2mb(B,A,Wo,Wt)
 [Num,Den,AllpassNum,AllpassDen] = iirlp2mb(B,A,Wo,Wt,Pass)

 Num,Den:               numerator,denominator of the transformed filter
 AllpassNum,AllpassDen: numerator,denominator of allpass transform,
 B,A:                   numerator,denominator of prototype low pass filter
 Wo:                    normalized_angular_frequency/pi to be transformed
 Wt:                    [phi=normalized_angular_frequencies]/pi target vector
 Pass:                  This parameter may have values 'pass' or 'stop'.  If
                        not given, it defaults to the value of 'pass'.

 With normalized ang. freq. targets 0 < phi(1) <  ... < phi(n) < pi radians

 for Pass == 'pass', the target multiband magnitude will be:
       --------       ----------        -----------...
      /        \     /          \      /            .
 0   phi(1) phi(2)  phi(3)   phi(4)   phi(5)   (phi(6))    pi

 for Pass == 'stop', the target multiband magnitude will be:
 -------      ---------        ----------...
        \    /         \      /           .
 0   phi(1) phi(2)  phi(3)   phi(4)  (phi(5))              pi

 Example of use:
 [B, A] = butter(6, 0.5);
 [Num, Den] = iirlp2mb(B, A, 0.5, [.2 .4 .6 .8]);



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
 IIR Low Pass Filter to Multiband Filter Transformation



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
impinvar


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 869
 -- Function File: [B_OUT, A_OUT] = impinvar (B, A, FS, TOL)
 -- Function File: [B_OUT, A_OUT] = impinvar (B, A, FS)
 -- Function File: [B_OUT, A_OUT] = impinvar (B, A)
     Converts analog filter with coefficients B and A to digital,
     conserving impulse response.

     If FS is not specified, or is an empty vector, it defaults to 1Hz.

     If TOL is not specified, it defaults to 0.0001 (0.1%) This function
     does the inverse of impinvar so that the following example should
     restore the original values of A and B.

     'invimpinvar' implements the reverse of this function.
          [b, a] = impinvar (b, a);
          [b, a] = invimpinvar (b, a);

     Reference: Thomas J. Cavicchi (1996) "Impulse invariance and
     multiple-order poles".  IEEE transactions on signal processing, Vol
     44 (9): 2344-2347

     See also: bilinear, invimpinvar.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Converts analog filter with coefficients B and A to digital, conserving
impulse 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
impz


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 744
 -- Function File: [X, T] = impz (B)
 -- Function File: [X, T] = impz (B, A)
 -- Function File: [X, T] = impz (B, A, N)
 -- Function File: [X, T] = impz (B, A, N, FS)
 -- Function File: impz (...)

     Generate impulse-response characteristics of the filter.  The
     filter coefficients correspond to the the z-plane rational function
     with numerator b and denominator a.  If a is not specified, it
     defaults to 1.  If n is not specified, or specified as [], it will
     be chosen such that the signal has a chance to die down to -120dB,
     or to not explode beyond 120dB, or to show five periods if there is
     no significant damping.  If no return arguments are requested, plot
     the results.

     See also: freqz, zplane.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
Generate impulse-response characteristics of the filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
interp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 733
 -- Function File: Y = interp (X, Q)
 -- Function File: Y = interp (X, Q, N)
 -- Function File: Y = interp (X, Q, N, WC)

     Upsample the signal x by a factor of q, using an order 2*q*n+1 FIR
     filter.  Note that q must be an integer for this rate change
     method.  n defaults to 4 and Wc defaults to 0.5.

     Example
          # Generate a signal.
          t=0:0.01:2; x=chirp(t,2,.5,10,'quadratic')+sin(2*pi*t*0.4);
          y = interp(x(1:4:length(x)),4,4,1);   # interpolate a sub-sample
          stem(t(1:121)*1000,x(1:121),"-g;Original;"); hold on;
          stem(t(1:121)*1000,y(1:121),"-r;Interpolated;");
          stem(t(1:4:121)*1000,x(1:4:121),"-b;Subsampled;"); hold off;

     See also: decimate, resample.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 74
Upsample the signal x by a factor of q, using an order 2*q*n+1 FIR
filter.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
invfreq


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1689
 usage: [B,A] = invfreq(H,F,nB,nA)
        [B,A] = invfreq(H,F,nB,nA,W)
        [B,A] = invfreq(H,F,nB,nA,W,[],[],plane)
        [B,A] = invfreq(H,F,nB,nA,W,iter,tol,plane)

 Fit filter B(z)/A(z) or B(s)/A(s) to complex frequency response at
 frequency points F. A and B are real polynomial coefficients of order
 nA and nB respectively.  Optionally, the fit-errors can be weighted vs
 frequency according to the weights W. Also, the transform plane can be
 specified as either 's' for continuous time or 'z' for discrete time. 'z'
 is chosen by default.  Eventually, Steiglitz-McBride iterations will be
 specified by iter and tol.

 H: desired complex frequency response
     It is assumed that A and B are real polynomials, hence H is one-sided.
 F: vector of frequency samples in radians
 nA: order of denominator polynomial A
 nB: order of numerator polynomial B
 plane='z': F on unit circle (discrete-time spectra, z-plane design)
 plane='s': F on jw axis     (continuous-time spectra, s-plane design)
 H(k) = spectral samples of filter frequency response at points zk,
  where zk=exp(sqrt(-1)*F(k)) when plane='z' (F(k) in [0,.5])
     and zk=(sqrt(-1)*F(k)) when plane='s' (F(k) nonnegative)
 Example:
     [B,A] = butter(12,1/4);
     [H,w] = freqz(B,A,128);
     [Bh,Ah] = invfreq(H,F,4,4);
     Hh = freqz(Bh,Ah);
     disp(sprintf('||frequency response error|| = %f',norm(H-Hh)));

 References: J. O. Smith, "Techniques for Digital Filter Design and System
      Identification with Application to the Violin, Ph.D. Dissertation,
      Elec. Eng. Dept., Stanford University, June 1983, page 50; or,

 http://ccrma.stanford.edu/~jos/filters/FFT_Based_Equation_Error_Method.html



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
 usage: [B,A] = invfreq(H,F,nB,nA)
        [B,A] = invfreq(H,F,nB,nA,W)
        



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
invfreqs


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 943
 Usage: [B,A] = invfreqs(H,F,nB,nA)
        [B,A] = invfreqs(H,F,nB,nA,W)
        [B,A] = invfreqs(H,F,nB,nA,W,iter,tol,'trace')

 Fit filter B(s)/A(s)to the complex frequency response H at frequency
 points F.  A and B are real polynomial coefficients of order nA and nB.
 Optionally, the fit-errors can be weighted vs frequency according to
 the weights W.
 Note: all the guts are in invfreq.m

 H: desired complex frequency response
 F: frequency (must be same length as H)
 nA: order of the denominator polynomial A
 nB: order of the numerator polynomial B
 W: vector of weights (must be same length as F)

 Example:
       B = [1/2 1];
       A = [1 1];
       w = linspace(0,4,128);
       H = freqs(B,A,w);
       [Bh,Ah] = invfreqs(H,w,1,1);
       Hh = freqs(Bh,Ah,w);
       plot(w,[abs(H);abs(Hh)])
       legend('Original','Measured');
       err = norm(H-Hh);
       disp(sprintf('L2 norm of frequency response error = %f',err));



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
 Usage: [B,A] = invfreqs(H,F,nB,nA)
        [B,A] = invfreqs(H,F,nB,nA,W)
      



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
invfreqz


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 820
 usage: [B,A] = invfreqz(H,F,nB,nA)
        [B,A] = invfreqz(H,F,nB,nA,W)
        [B,A] = invfreqz(H,F,nB,nA,W,iter,tol,'trace')

 Fit filter B(z)/A(z)to the complex frequency response H at frequency
 points F.  A and B are real polynomial coefficients of order nA and nB.
 Optionally, the fit-errors can be weighted vs frequency according to
 the weights W.
 Note: all the guts are in invfreq.m

 H: desired complex frequency response
 F: normalized frequency (0 to pi) (must be same length as H)
 nA: order of the denominator polynomial A
 nB: order of the numerator polynomial B
 W: vector of weights (must be same length as F)

 Example:
     [B,A] = butter(4,1/4);
     [H,F] = freqz(B,A);
     [Bh,Ah] = invfreq(H,F,4,4);
     Hh = freqz(Bh,Ah);
     disp(sprintf('||frequency response error|| = %f',norm(H-Hh)));



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
 usage: [B,A] = invfreqz(H,F,nB,nA)
        [B,A] = invfreqz(H,F,nB,nA,W)
      



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
invimpinvar


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 815
 -- Function File: [B_OUT, A_OUT] = invimpinvar (B, A, FS, TOL)
 -- Function File: [B_OUT, A_OUT] = invimpinvar (B, A, FS)
 -- Function File: [B_OUT, A_OUT] = invimpinvar (B, A)
     Converts digital filter with coefficients B and A to analog,
     conserving impulse response.

     This function does the inverse of impinvar so that the following
     example should restore the original values of A and B.
          [b, a] = impinvar (b, a);
          [b, a] = invimpinvar (b, a);

     If FS is not specified, or is an empty vector, it defaults to 1Hz.

     If TOL is not specified, it defaults to 0.0001 (0.1%)

     Reference: Thomas J. Cavicchi (1996) "Impulse invariance and
     multiple-order poles".  IEEE transactions on signal processing, Vol
     40 (9): 2344-2347

     See also: bilinear, impinvar.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Converts digital filter with coefficients B and A to analog, conserving
impulse 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
kaiser


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 637
 -- Function File: kaiser (M)
 -- Function File: kaiser (M, BETA)

     Return the filter coefficients of a Kaiser window of length M.  The
     Fourier transform of the window has a stop-band attenuation that is
     derived from the parameter BETA.

     For the definition of the Kaiser window, see A. V. Oppenheim & R.
     W. Schafer, "Discrete-Time Signal Processing".

     The continuous version of width m centered about x=0 is:

                  besseli(0, beta * sqrt(1-(2*x/m).^2))
          k(x) =  -------------------------------------,  m/2 <= x <= m/2
                         besseli(0, beta)

     See also: kaiserord.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Return the filter coefficients of a Kaiser window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
kaiserord


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1723
 -- Function File: [N, WN, BETA, FTYPE] = kaiserord (F, M, DEV)
 -- Function File: [...] = kaiserord (F, M, DEV, FS)

     Return the parameters needed to produce a filter of the desired
     specification from a Kaiser window.  The vector F contains pairs of
     frequency band edges in the range [0,1].  The vector M specifies
     the magnitude response for each band.  The values of M must be zero
     for all stop bands and must have the same magnitude for all pass
     bands.  The deviation of the filter DEV can be specified as a
     scalar or a vector of the same length as M.  The optional sampling
     rate FS can be used to indicate that F is in Hz in the range
     [0,FS/2].

     The returned value N is the required order of the filter (the
     length of the filter minus 1).  The vector WN contains the band
     edges of the filter suitable for passing to 'fir1'.  The value BETA
     is the parameter of the Kaiser window of length N+1 to shape the
     filter.  The string FTYPE contains the type of filter to specify to
     'fir1'.

     The Kaiser window parameters n and beta are computed from the
     relation between ripple (A=-20*log10(dev)) and transition width (dw
     in radians) discovered empirically by Kaiser:

                    / 0.1102(A-8.7)                        A > 50
             beta = | 0.5842(A-21)^0.4 + 0.07886(A-21)     21 <= A <= 50
                    \ 0.0                                  A < 21

             n = (A-8)/(2.285 dw)

     Example:
          [n, w, beta, ftype] = kaiserord ([1000, 1200], [1, 0], [0.05, 0.05], 11025);
          b = fir1 (n, w, kaiser (n+1, beta), ftype, "noscale");
          freqz (b, 1, [], 11025);

     See also: fir1, kaiser.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return the parameters needed to produce a filter of the desired
specification fr



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
levinson


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 892
 -- Function File: [A, V, REF] = levinson (ACF)
 -- Function File: [...] = levinson (ACF, P)

     Use the Durbin-Levinson algorithm to solve: toeplitz(acf(1:p)) * x
     = -acf(2:p+1).  The solution [1, x'] is the denominator of an all
     pole filter approximation to the signal x which generated the
     autocorrelation function acf.

     acf is the autocorrelation function for lags 0 to p.  p defaults to
     length(acf)-1.  Returns a=[1, x'] the denominator filter
     coefficients.  v= variance of the white noise = square of the
     numerator constant ref = reflection coefficients = coefficients of
     the lattice implementation of the filter Use freqz(sqrt(v),a) to
     plot the power spectrum.

     REFERENCE [1] Steven M. Kay and Stanley Lawrence Marple Jr.:
     "Spectrum analysis - a modern perspective", Proceedings of the
     IEEE, Vol 69, pp 1380-1419, Nov., 1981


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Use the Durbin-Levinson algorithm to solve: toeplitz(acf(1:p)) * x =
-acf(2:p+1)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
marcumq


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 958
 -- Function File: Q = marcumq (A, B)
 -- Function File: Q = marcumq (A, B, M)
 -- Function File: Q = marcumq (A, B, M, TOL)

     Compute the generalized Marcum Q function of order M with
     noncentrality parameter A and argument B.  If the order M is
     omitted it defaults to 1.  An optional relative tolerance TOL may
     be included, the default is 'eps'.

     If the input arguments are commensurate vectors, this function will
     produce a table of values.

     This function computes Marcum's Q function using the infinite
     Bessel series, truncated when the relative error is less than the
     specified tolerance.  The accuracy is limited by that of the Bessel
     functions, so reducing the tolerance is probably not useful.

     Reference: Marcum, "Tables of Q Functions", Rand Corporation.

     Reference: R.T. Short, "Computation of Noncentral Chi-squared and
     Rice Random Variables", www.phaselockedsystems.com/publications


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the generalized Marcum Q function of order M with noncentrality
paramete



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
mexihat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 87
 -- Function File: [PSI, X] = mexihat (LB, UB, N)
     Compute the Mexican hat wavelet.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
Compute the Mexican hat wavelet.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
meyeraux


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 86
 -- Function File: Y = meyeraux (X)
     Compute the Meyer wavelet auxiliary function.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
Compute the Meyer wavelet auxiliary function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
morlet


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 81
 -- Function File: [PSI, X] = morlet (LB, UB, N)
     Compute the Morlet wavelet.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
Compute the Morlet wavelet.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
movingrms


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 392
 -- Function File: [RMSX,W] = movingrms (X,W,RC,FS=1)
     Calculate moving RMS value of the signal in X.

     The signal is convoluted against a sigmoid window of width W and
     risetime RC.  The units of these parameters are relative to the
     value of the sampling frequency given in FS (Default value = 1).

     Run 'demo movingrms' to see an example.

     See also: sigmoid_train.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Calculate moving RMS value of the signal in X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
mscohere


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 550
 -- Function File: [PXX, FREQ] = mscohere (X, Y)
 -- Function File: [...] = mscohere (X, Y, WINDOW)
 -- Function File: [...] = mscohere (X, Y, WINDOW, OVERLAP)
 -- Function File: [...] = mscohere (X, Y, WINDOW, OVERLAP, NFFT)
 -- Function File: [...] = mscohere (X, Y, WINDOW, OVERLAP, NFFT, FS)
 -- Function File: [...] = mscohere (X, Y, WINDOW, OVERLAP, NFFT, FS,
          RANGE)
 -- Function File: mscohere (...)

     Estimate (mean square) coherence of signals X and Y.  Use the Welch
     (1967) periodogram/FFT method.

     See also: pwelch.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Estimate (mean square) coherence of signals X and Y.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
ncauer


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 380
 usage: [Zz, Zp, Zg] = ncauer(Rp, Rs, n)

 Analog prototype for Cauer filter.
 [z, p, g]=ncauer(Rp, Rs, ws)
 Rp = Passband ripple
 Rs = Stopband ripple
 Ws = Desired order

 References:

 - Serra, Celso Penteado, Teoria e Projeto de Filtros, Campinas: CARTGRAF,
   1983.
 - Lamar, Marcus Vinicius, Notas de aula da disciplina TE 456 - Circuitos
   Analogicos II, UFPR, 2001/2002.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
 usage: [Zz, Zp, Zg] = ncauer(Rp, Rs, n)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nuttallwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 559
 -- Function File: nuttallwin (M)
 -- Function File: nuttallwin (M, "periodic")
 -- Function File: nuttallwin (M, "symmetric")
     Return the filter coefficients of a Blackman-Harris window defined
     by Nuttall of length M.

     If the optional argument '"periodic"' is given, the periodic form
     of the window is returned.  This is equivalent to the window of
     length M+1 with the last coefficient removed.  The optional
     argument '"symmetric"' is equivalent to not specifying a second
     argument.

     See also: blackman, blackmanharris.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return the filter coefficients of a Blackman-Harris window defined by
Nuttall of



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
parzenwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 135
 -- Function File: parzenwin (M)
     Return the filter coefficients of a Parzen window of length M.

     See also: rectwin, bartlett.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Return the filter coefficients of a Parzen window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
pburg


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3777
 usage:
    [psd,f_out] = pburg(x,poles,freq,Fs,range,method,plot_type,criterion)

 Calculate Burg maximum-entropy power spectral density.
 The functions "arburg" and "ar_psd" do all the work.
 See "help arburg" and "help ar_psd" for further details.

 ARGUMENTS:
     All but the first two arguments are optional and may be empty.
   x       %% [vector] sampled data

   poles   %% [integer scalar] required number of poles of the AR model

   freq    %% [real vector] frequencies at which power spectral density
           %%               is calculated
           %% [integer scalar] number of uniformly distributed frequency
           %%          values at which spectral density is calculated.
           %%          [default=256]

   Fs      %% [real scalar] sampling frequency (Hertz) [default=1]


 CONTROL-STRING ARGUMENTS -- each of these arguments is a character string.
   Control-string arguments can be in any order after the other arguments.


   range   %% 'half',  'onesided' : frequency range of the spectrum is
           %%       from zero up to but not including sample_f/2.  Power
           %%       from negative frequencies is added to the positive
           %%       side of the spectrum.
           %% 'whole', 'twosided' : frequency range of the spectrum is
           %%       -sample_f/2 to sample_f/2, with negative frequencies
           %%       stored in "wrap around" order after the positive
           %%       frequencies; e.g. frequencies for a 10-point 'twosided'
           %%       spectrum are 0 0.1 0.2 0.3 0.4 0.5 -0.4 -0.3 -0.2 -0.1
           %% 'shift', 'centerdc' : same as 'whole' but with the first half
           %%       of the spectrum swapped with second half to put the
           %%       zero-frequency value in the middle. (See "help
           %%       fftshift". If "freq" is vector, 'shift' is ignored.
           %% If model coefficients "ar_coeffs" are real, the default
           %% range is 'half', otherwise default range is 'whole'.

   method  %% 'fft':  use FFT to calculate power spectral density.
           %% 'poly': calculate spectral density as a polynomial of 1/z
           %% N.B. this argument is ignored if the "freq" argument is a
           %%      vector.  The default is 'poly' unless the "freq"
           %%      argument is an integer power of 2.

 plot_type %% 'plot', 'semilogx', 'semilogy', 'loglog', 'squared' or 'db':
           %% specifies the type of plot.  The default is 'plot', which
           %% means linear-linear axes. 'squared' is the same as 'plot'.
           %% 'dB' plots "10*log10(psd)".  This argument is ignored and a
           %% spectrum is not plotted if the caller requires a returned
           %% value.

 criterion %% [optional string arg]  model-selection criterion.  Limits
           %%       the number of poles so that spurious poles are not
           %%       added when the whitened data has no more information
           %%       in it (see Kay & Marple, 1981). Recognized values are
           %%  'AKICc' -- approximate corrected Kullback information
           %%             criterion (recommended),
           %%   'KIC'  -- Kullback information criterion
           %%   'AICc' -- corrected Akaike information criterion
           %%   'AIC'  -- Akaike information criterion
           %%   'FPE'  -- final prediction error" criterion
           %% The default is to NOT use a model-selection criterion

 RETURNED VALUES:
     If return values are not required by the caller, the spectrum
     is plotted and nothing is returned.
   psd       %% [real vector] power-spectral density estimate
   f_out     %% [real vector] frequency values

 HINTS
   This function is a wrapper for arburg and ar_psd.
   See "help arburg", "help ar_psd".



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
 usage:
    [psd,f_out] = pburg(x,poles,freq,Fs,range,method,plot_type,criterion



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
pei_tseng_notch


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 691
 -- Function File: [B, A] = pei_tseng_notch (FREQUENCIES, BANDWIDTHS)
     Return coefficients for an IIR notch-filter with one or more filter
     frequencies and according (very narrow) bandwidths to be used with
     'filter' or 'filtfilt'.  The filter construction is based on an
     allpass which performs a reversal of phase at the filter
     frequencies.  Thus, the mean of the phase-distorted and the
     original signal has the respective frequencies removed.  See the
     demo for an illustration.

     Original source: Pei, Soo-Chang, and Chien-Cheng Tseng "IIR
     Multiple Notch Filter Design Based on Allpass Filter" 1996 IEEE
     Tencon doi: 10.1109/TENCON.1996.608814)


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return coefficients for an IIR notch-filter with one or more filter
frequencies 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
polystab


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 156
 b = polystab(a)

 Stabilize the polynomial transfer function by replacing all roots
 outside the unit circle with their reflection inside the unit circle.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
 b = polystab(a)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
primitive


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 743
 -- Function File: F = primitive (F, T, F0)
     Calculates the primitive of a function.

     The function approximates the primitive (indefinite integral) of
     the univariate function handle F with constant of integration F0.
     The output is the primitive evaluated at the points T.  The vector
     T must be ordered and ascending.

     This function is a fancy way of calculating the cumulative sum,

     'F = cumsum (f(t).*diff (t)([1 1:end]))'.

     Example:
          f = @(t) sin(2*pi*3*t);
          t = [0; sort(rand(100,1))];
          F = primitive (f,t,0);
          t_true = linspace(0,1,1e3).';
          F_true = (1 - cos(2*pi*3*t_true))/(2*pi*3);
          plot (t,F,'.',t_true,F_true)

     See also: quadgk, cumsum.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Calculates the primitive of a function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
pulstran


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1434
 -- Function File: Y = pulstran (T, D, FUNC, ...)
 -- Function File: Y = pulstran (T, D, P)
 -- Function File: Y = pulstran (T, D, P, FS)
 -- Function File: Y = pulstran (T, D, P, FS, METHOD)

     Generate the signal y=sum(func(t+d,...))  for each d.  If d is a
     matrix of two columns, the first column is the delay d and the
     second column is the amplitude a, and y=sum(a*func(t+d)) for each
     d,a.  Clearly, func must be a function which accepts a vector of
     times.  Any extra arguments needed for the function must be tagged
     on the end.

     Example:
          fs = 11025;  # arbitrary sample rate
          f0 = 100;    # pulse train sample rate
          w = 0.001;   # pulse width of 1 millisecond
          auplot (pulstran (0:1/fs:0.1, 0:1/f0:0.1, "rectpuls", w), fs);

     If instead of a function name you supply a pulse shape sampled at
     frequency Fs (default 1 Hz), an interpolated version of the pulse
     is added at each delay d.  The interpolation stays within the the
     time range of the delayed pulse.  The interpolation method defaults
     to linear, but it can be any interpolation method accepted by the
     function interp1.

     Example:
          fs = 11025;      # arbitrary sample rate
          f0 = 100;        # pulse train sample rate
          w = boxcar(10);  # pulse width of 1 millisecond at 10 kHz
          auplot (pulstran (0:1/fs:0.1, 0:1/f0:0.1, w, 10000), fs);


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
Generate the signal y=sum(func(t+d,...))  for each d.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
pwelch


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7135
 USAGE:
   [spectra,freq] = pwelch(x,window,overlap,Nfft,Fs,
                           range,plot_type,detrend,sloppy)
     Estimate power spectral density of data "x" by the Welch (1967)
     periodogram/FFT method.  All arguments except "x" are optional.
         The data is divided into segments.  If "window" is a vector, each
     segment has the same length as "window" and is multiplied by "window"
     before (optional) zero-padding and calculation of its periodogram. If
     "window" is a scalar, each segment has a length of "window" and a
     Hamming window is used.
         The spectral density is the mean of the periodograms, scaled so that
     area under the spectrum is the same as the mean square of the
     data.  This equivalence is supposed to be exact, but in practice there
     is a mismatch of up to 0.5% when comparing area under a periodogram
     with the mean square of the data.

  [spectra,freq] = pwelch(x,y,window,overlap,Nfft,Fs,
                          range,plot_type,detrend,sloppy,results)
     Two-channel spectrum analyser.  Estimate power spectral density, cross-
     spectral density, transfer function and/or coherence functions of time-
     series input data "x" and output data "y" by the Welch (1967)
     periodogram/FFT method.
       pwelch treats the second argument as "y" if there is a control-string
     argument "cross", "trans", "coher" or "ypower"; "power" does not force
     the 2nd argument to be treated as "y".  All other arguments are
     optional.  All spectra are returned in matrix "spectra".

  [spectra,Pxx_ci,freq] = pwelch(x,window,overlap,Nfft,Fs,conf,
                                 range,plot_type,detrend,sloppy)
  [spectra,Pxx_ci,freq] = pwelch(x,y,window,overlap,Nfft,Fs,conf,
                                 range,plot_type,detrend,sloppy,results)
     Estimates confidence intervals for the spectral density.
     See Hint (7) below for compatibility options.  Confidence level "conf"
     is the 6th or 7th numeric argument.  If "results" control-string
     arguments are used, one of them must be "power" when the "conf"
     argument is present; pwelch can estimate confidence intervals only for
     the power spectrum of the "x" data.  It does not know how to estimate
     confidence intervals of the cross-power spectrum, transfer function or
     coherence; if you can suggest a good method, please send a bug report.

 ARGUMENTS
 All but the first argument are optional and may be empty, except that
 the "results" argument may require the second argument to be "y".

 x           %% [non-empty vector] system-input time-series data
 y           %% [non-empty vector] system-output time-series data

 window      %% [real vector] of window-function values between 0 and 1; the
             %%       data segment has the same length as the window.
             %%       Default window shape is Hamming.
             %% [integer scalar] length of each data segment.  The default
             %%       value is window=sqrt(length(x)) rounded up to the
             %%       nearest integer power of 2; see 'sloppy' argument.

 overlap     %% [real scalar] segment overlap expressed as a multiple of
             %%       window or segment length.   0 <= overlap < 1,
             %%       The default is overlap=0.5 .

 Nfft        %% [integer scalar] Length of FFT.  The default is the length
             %%       of the "window" vector or has the same value as the
             %%       scalar "window" argument.  If Nfft is larger than the
             %%       segment length, "seg_len", the data segment is padded
             %%       with "Nfft-seg_len" zeros.  The default is no padding.
             %%       Nfft values smaller than the length of the data
             %%       segment (or window) are ignored silently.

 Fs          %% [real scalar] sampling frequency (Hertz); default=1.0

 conf        %% [real scalar] confidence level between 0 and 1.  Confidence
             %%       intervals of the spectral density are estimated from
             %%       scatter in the periodograms and are returned as Pxx_ci.
             %%       Pxx_ci(:,1) is the lower bound of the confidence
             %%       interval and Pxx_ci(:,2) is the upper bound.  If there
             %%       are three return values, or conf is an empty matrix,
             %%       confidence intervals are calculated for conf=0.95 .
             %%       If conf is zero or is not given, confidence intervals
             %%       are not calculated. Confidence intervals can be
             %%       obtained only for the power spectral density of x;
             %%       nothing else.

 CONTROL-STRING ARGUMENTS -- each of these arguments is a character string.
   Control-string arguments must be after the other arguments but can be in
   any order.

 range     %% 'half',  'onesided' : frequency range of the spectrum is
           %%       zero up to but not including Fs/2.  Power from
           %%       negative frequencies is added to the positive side of
           %%       the spectrum, but not at zero or Nyquist (Fs/2)
           %%       frequencies.  This keeps power equal in time and
           %%       spectral domains.  See reference [2].
           %% 'whole', 'twosided' : frequency range of the spectrum is
           %%       -Fs/2 to Fs/2, with negative frequencies
           %%       stored in "wrap around" order after the positive
           %%       frequencies; e.g. frequencies for a 10-point 'twosided'
           %%       spectrum are 0 0.1 0.2 0.3 0.4 0.5 -0.4 -0.3 -0.2 -0.1
           %% 'shift', 'centerdc' : same as 'whole' but with the first half
           %%       of the spectrum swapped with second half to put the
           %%       zero-frequency value in the middle. (See "help
           %%       fftshift".
           %% If data (x and y) are real, the default range is 'half',
           %% otherwise default range is 'whole'.

 plot_type %% 'plot', 'semilogx', 'semilogy', 'loglog', 'squared' or 'db':
           %% specifies the type of plot.  The default is 'plot', which
           %% means linear-linear axes. 'squared' is the same as 'plot'.
           %% 'dB' plots "10*log10(psd)".  This argument is ignored and a
           %% spectrum is not plotted if the caller requires a returned
           %% value.

 detrend   %% 'no-strip', 'none' -- do NOT remove mean value from the data
           %% 'short', 'mean' -- remove the mean value of each segment from
           %%                    each segment of the data.
           %% 'linear',       -- remove linear trend from each segment of
           %%                    the data.
           %% 'long-mean'     -- remove the mean value from the data before
           %%              splitting it into segments.  This is the default.

   sloppy  %% 'sloppy': FFT length is rounded up to the nearest integer
           %%       power of 2 by zero padding.  FFT length is adjusted
           %%       after addition of padding by explicit Nfft argument.
           %%       The default is to use exactly the FFT and window/



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
 USAGE:
   [spectra,freq] = pwelch(x,window,overlap,Nfft,Fs,
                   



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
pyulear


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3135
 usage:
    [psd,f_out] = pyulear(x,poles,freq,Fs,range,method,plot_type)

 Calculates a Yule-Walker autoregressive (all-pole) model of the data "x"
 and computes the power spectrum of the model.  This is a wrapper for
 functions "aryule" and "ar_psd" which perform the argument checking.
 See "help aryule" and "help ar_psd" for further details.

 ARGUMENTS:
     All but the first two arguments are optional and may be empty.
   x       %% [vector] sampled data

   poles   %% [integer scalar] required number of poles of the AR model

   freq    %% [real vector] frequencies at which power spectral density
           %%               is calculated
           %% [integer scalar] number of uniformly distributed frequency
           %%          values at which spectral density is calculated.
           %%          [default=256]

   Fs      %% [real scalar] sampling frequency (Hertz) [default=1]


 CONTROL-STRING ARGUMENTS -- each of these arguments is a character string.
   Control-string arguments can be in any order after the other arguments.


   range   %% 'half',  'onesided' : frequency range of the spectrum is
           %%       from zero up to but not including sample_f/2.  Power
           %%       from negative frequencies is added to the positive
           %%       side of the spectrum.
           %% 'whole', 'twosided' : frequency range of the spectrum is
           %%       -sample_f/2 to sample_f/2, with negative frequencies
           %%       stored in "wrap around" order after the positive
           %%       frequencies; e.g. frequencies for a 10-point 'twosided'
           %%       spectrum are 0 0.1 0.2 0.3 0.4 0.5 -0.4 -0.3 -0.2 -0.1
           %% 'shift', 'centerdc' : same as 'whole' but with the first half
           %%       of the spectrum swapped with second half to put the
           %%       zero-frequency value in the middle. (See "help
           %%       fftshift". If "freq" is vector, 'shift' is ignored.
           %% If model coefficients "ar_coeffs" are real, the default
           %% range is 'half', otherwise default range is 'whole'.

   method  %% 'fft':  use FFT to calculate power spectrum.
           %% 'poly': calculate power spectrum as a polynomial of 1/z
           %% N.B. this argument is ignored if the "freq" argument is a
           %%      vector.  The default is 'poly' unless the "freq"
           %%      argument is an integer power of 2.

 plot_type %% 'plot', 'semilogx', 'semilogy', 'loglog', 'squared' or 'db':
           %% specifies the type of plot.  The default is 'plot', which
           %% means linear-linear axes. 'squared' is the same as 'plot'.
           %% 'dB' plots "10*log10(psd)".  This argument is ignored and a
           %% spectrum is not plotted if the caller requires a returned
           %% value.

 RETURNED VALUES:
     If return values are not required by the caller, the spectrum
     is plotted and nothing is returned.
   psd     %% [real vector] power-spectrum estimate
   f_out   %% [real vector] frequency values

 HINTS
   This function is a wrapper for aryule and ar_psd.
   See "help aryule", "help ar_psd".



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
 usage:
    [psd,f_out] = pyulear(x,poles,freq,Fs,range,method,plot_type)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
qp_kaiser


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 691
 -- Function File: qp_kaiser (NB, AT)
 -- Function File: qp_kaiser (NB, AT, LINEAR)

     Computes a finite impulse response (FIR) filter for use with a
     quasi-perfect reconstruction polyphase-network filter bank.  This
     version utilizes a Kaiser window to shape the frequency response of
     the designed filter.  Tha number nb of bands and the desired
     attenuation at in the stop-band are given as parameters.

     The Kaiser window is multiplied by the ideal impulse response
     h(n)=a.sinc(a.n) and converted to its minimum-phase version by
     means of a Hilbert transform.

     By using a third non-null argument, the minimum-phase calculation
     is omitted at all.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Computes a finite impulse response (FIR) filter for use with a
quasi-perfect rec



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
rceps


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 816
 -- Function File: [Y, XM] = rceps (X)
     Produce the cepstrum of the signal x, and if desired, the minimum
     phase reconstruction of the signal x.  If x is a matrix, do so for
     each column of the matrix.

     Example:
          f0 = 70; Fs = 10000;                   # 100 Hz fundamental, 10kHz sampling rate
          a = poly (0.985 * exp (1i*pi*[0.1, -0.1, 0.3, -0.3])); # two formants
          s = 0.005 * randn (1024, 1);           # Noise excitation signal
          s(1:Fs/f0:length(s)) = 1;              # Impulse glottal wave
          x = filter (1, a, s);                  # Speech signal in x
          [y, xm] = rceps (x .* hanning (1024)); # cepstrum and min phase reconstruction

     Reference Programs for digital signal processing.  IEEE Press.  New
     York: John Wiley & Sons.  1979.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Produce the cepstrum of the signal x, and if desired, the minimum phase
reconstr



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
rectpuls


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 528
 -- Function File: Y = rectpuls (T)
 -- Function File: Y = rectpuls (T, W)

     Generate a rectangular pulse over the interval [-W/2,W/2), sampled
     at times T.  This is useful with the function 'pulstran' for
     generating a series pulses.

     Example:
          fs = 11025;  # arbitrary sample rate
          f0 = 100;    # pulse train sample rate
          w = 0.3/f0;  # pulse width 3/10th the distance between pulses
          auplot(pulstran(0:1/fs:4/f0, 0:1/f0:4/f0, 'rectpuls', w), fs);

     See also: pulstran.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 78
Generate a rectangular pulse over the interval [-W/2,W/2), sampled at
times T.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
rectwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 145
 -- Function File: rectwin (M)
     Return the filter coefficients of a rectangular window of length M.

     See also: boxcar, hamming, hanning.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
Return the filter coefficients of a rectangular window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
resample


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 648
 -- Function File: [Y, H] = resample (X, P, Q)
 -- Function File: Y = resample (X, P, Q, H)
     Change the sample rate of X by a factor of P/Q.  This is performed
     using a polyphase algorithm.  The impulse response H of the
     antialiasing filter is either specified or either designed with a
     Kaiser-windowed sinecard.

     Ref [1] J. G. Proakis and D. G. Manolakis, Digital Signal
     Processing: Principles, Algorithms, and Applications, 4th ed.,
     Prentice Hall, 2007.  Chap.  6

     Ref [2] A. V. Oppenheim, R. W. Schafer and J. R. Buck,
     Discrete-time signal processing, Signal processing series,
     Prentice-Hall, 1999


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Change the sample rate of X by a factor of P/Q.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
residued


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1044
 -- Function File: [R, P, F, M] = residued (B, A)
     Compute the partial fraction expansion (PFE) of filter H(z) =
     B(z)/A(z).  In the usual PFE function 'residuez', the IIR part
     (poles P and residues R) is driven _in parallel_ with the FIR part
     (F).  In this variant, the IIR part is driven by the _output_ of
     the FIR part.  This structure can be more accurate in signal
     modeling applications.

     INPUTS: B and A are vectors specifying the digital filter H(z) =
     B(z)/A(z).  See 'help filter' for documentation of the B and A
     filter coefficients.

     RETURNED:
        * R = column vector containing the filter-pole residues
        * P = column vector containing the filter poles
        * F = row vector containing the FIR part, if any
        * M = column vector of pole multiplicities

     EXAMPLES:
          See test residued verbose to see a number of examples.

     For the theory of operation, see
     'http://ccrma.stanford.edu/~jos/filters/residued.html'

     See also: residue, residued.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
Compute the partial fraction expansion (PFE) of filter H(z) = B(z)/A(z).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
residuez


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 745
 -- Function File: [R, P, F, M] = residuez (B, A)
     Compute the partial fraction expansion of filter H(z) = B(z)/A(z).

     INPUTS: B and A are vectors specifying the digital filter H(z) =
     B(z)/A(z).  See 'help filter' for documentation of the B and A
     filter coefficients.

     RETURNED:
        * R = column vector containing the filter-pole residues
        * P = column vector containing the filter poles
        * F = row vector containing the FIR part, if any
        * M = column vector of pole multiplicities

     EXAMPLES:
          See test residuez verbose to see a number of examples.

     For the theory of operation, see
     'http://ccrma.stanford.edu/~jos/filters/residuez.html'

     See also: residue, residued.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Compute the partial fraction expansion of filter H(z) = B(z)/A(z).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
sampled2continuous


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 424
 -- Function File: XT = sampled2continuous (XN, T, T)

     Calculate the x(t) reconstructed from samples x[n] sampled at a
     rate 1/T samples per unit time.

     t is all the instants of time when you need x(t) from x[n]; this
     time is relative to x[0] and not an absolute time.

     This function can be used to calculate sampling rate effects on
     aliasing, actual signal reconstruction from discrete samples.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Calculate the x(t) reconstructed from samples x[n] sampled at a rate 1/T
samples



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
sawtooth


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 661
 -- Function File: Y = sawtooth (T)
 -- Function File: Y = sawtooth (T, WIDTH)
     Generates a sawtooth wave of period '2 * pi' with limits '+1/-1'
     for the elements of T.

     WIDTH is a real number between '0' and '1' which specifies the
     point between '0' and '2 * pi' where the maximum is.  The function
     increases linearly from '-1' to '1' in '[0, 2 * pi * WIDTH]'
     interval, and decreases linearly from '1' to '-1' in the interval
     '[2 * pi * WIDTH, 2 * pi]'.

     If WIDTH is 0.5, the function generates a standard triangular wave.

     If WIDTH is not specified, it takes a value of 1, which is a
     standard sawtooth function.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Generates a sawtooth wave of period '2 * pi' with limits '+1/-1' for the
element



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
schtrig


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 356
 -- Function File: [RMSX,W] = schtrig (X,LVL,RST=1)
     Implements a multisignal Schmitt trigger with levels LVL.

     The triger works along the first dimension of the array X.  When
     'RST==1' the state of the trigger for all signals is set to the low
     state (i.e.  0).

     Run 'demo schtrig' to see an example.

     See also: clustersegment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
Implements a multisignal Schmitt trigger with levels LVL.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
sftrans


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4017
 -- Function File: [SZ, SP, SG] = sftrans (SZ, SP, SG, W, STOP)

     Transform band edges of a generic lowpass filter (cutoff at W=1)
     represented in splane zero-pole-gain form.  W is the edge of the
     target filter (or edges if band pass or band stop).  Stop is true
     for high pass and band stop filters or false for low pass and band
     pass filters.  Filter edges are specified in radians, from 0 to pi
     (the nyquist frequency).

     Theory: Given a low pass filter represented by poles and zeros in
     the splane, you can convert it to a low pass, high pass, band pass
     or band stop by transforming each of the poles and zeros
     individually.  The following table summarizes the transformation:

          Transform         Zero at x                  Pole at x
          ----------------  -------------------------  ------------------------
          Low Pass          zero: Fc x/C               pole: Fc x/C
          S -> C S/Fc       gain: C/Fc                 gain: Fc/C
          ----------------  -------------------------  ------------------------
          High Pass         zero: Fc C/x               pole: Fc C/x
          S -> C Fc/S       pole: 0                    zero: 0
                            gain: -x                   gain: -1/x
          ----------------  -------------------------  ------------------------
          Band Pass         zero: b +- sqrt(b^2-FhFl)  pole: b +- sqrt(b^2-FhFl)
                 S^2+FhFl   pole: 0                    zero: 0
          S -> C --------   gain: C/(Fh-Fl)            gain: (Fh-Fl)/C
                 S(Fh-Fl)   b=x/C (Fh-Fl)/2            b=x/C (Fh-Fl)/2
          ----------------  -------------------------  ------------------------
          Band Stop         zero: b +- sqrt(b^2-FhFl)  pole: b +- sqrt(b^2-FhFl)
                 S(Fh-Fl)   pole: +-sqrt(-FhFl)        zero: +-sqrt(-FhFl)
          S -> C --------   gain: -x                   gain: -1/x
                 S^2+FhFl   b=C/x (Fh-Fl)/2            b=C/x (Fh-Fl)/2
          ----------------  -------------------------  ------------------------
          Bilinear          zero: (2+xT)/(2-xT)        pole: (2+xT)/(2-xT)
               2 z-1        pole: -1                   zero: -1
          S -> - ---        gain: (2-xT)/T             gain: (2-xT)/T
               T z+1
          ----------------  -------------------------  ------------------------

     where C is the cutoff frequency of the initial lowpass filter, Fc
     is the edge of the target low/high pass filter and [Fl,Fh] are the
     edges of the target band pass/stop filter.  With abundant tedious
     algebra, you can derive the above formulae yourself by substituting
     the transform for S into H(S)=S-x for a zero at x or H(S)=1/(S-x)
     for a pole at x, and converting the result into the form:

             H(S)=g prod(S-Xi)/prod(S-Xj)

     The transforms are from the references.  The actual pole-zero-gain
     changes I derived myself.

     Please note that a pole and a zero at the same place exactly
     cancel.  This is significant for High Pass, Band Pass and Band Stop
     filters which create numerous extra poles and zeros, most of which
     cancel.  Those which do not cancel have a "fill-in" effect,
     extending the shorter of the sets to have the same number of as the
     longer of the sets of poles and zeros (or at least split the
     difference in the case of the band pass filter).  There may be
     other opportunistic cancellations but I will not check for them.

     Also note that any pole on the unit circle or beyond will result in
     an unstable filter.  Because of cancellation, this will only happen
     if the number of poles is smaller than the number of zeros and the
     filter is high pass or band pass.  The analytic design methods all
     yield more poles than zeros, so this will not be a problem.

     References:

     Proakis & Manolakis (1992).  Digital Signal Processing.  New York:
     Macmillan Publishing Company.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Transform band edges of a generic lowpass filter (cutoff at W=1)
represented in 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
sgolay


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1236
 -- Function File: F = sgolay (P, N)
 -- Function File: F = sgolay (P, N, M)
 -- Function File: F = sgolay (P, N, M, TS)
     Computes the filter coefficients for all Savitzsky-Golay smoothing
     filters of order p for length n (odd).  m can be used in order to
     get directly the mth derivative.  In this case, ts is a scaling
     factor.

     The early rows of F smooth based on future values and later rows
     smooth based on past values, with the middle row using half future
     and half past.  In particular, you can use row i to estimate x(k)
     based on the i-1 preceding values and the n-i following values of x
     values as y(k) = F(i,:) * x(k-i+1:k+n-i).

     Normally, you would apply the first (n-1)/2 rows to the first k
     points of the vector, the last k rows to the last k points of the
     vector and middle row to the remainder, but for example if you were
     running on a realtime system where you wanted to smooth based on
     the all the data collected up to the current time, with a lag of
     five samples, you could apply just the filter on row n-5 to your
     window of length n each time you added a new sample.

     Reference: Numerical recipes in C. p 650

     See also: sgolayfilt.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Computes the filter coefficients for all Savitzsky-Golay smoothing
filters of or



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
sgolayfilt


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1214
 -- Function File: Y = sgolayfilt (X)
 -- Function File: Y = sgolayfilt (X, P)
 -- Function File: Y = sgolayfilt (X, P, N)
 -- Function File: Y = sgolayfilt (X, P, N, M)
 -- Function File: Y = sgolayfilt (X, P, N, M, TS)
 -- Function File: Y = sgolayfilt (X, P, N, M, TS)
 -- Function File: Y = sgolayfilt (X, F)
     Smooth the data in x with a Savitsky-Golay smoothing filter of
     polynomial order p and length n, n odd, n > p.  By default, p=3 and
     n=p+2 or n=p+3 if p is even.

     If F is given as a matrix, it is expected to be a filter as
     computed by 'sgolay'.

     These filters are particularly good at preserving lineshape while
     removing high frequency squiggles.  Particularly, compare a 5
     sample averager, an order 5 butterworth lowpass filter (cutoff 1/3)
     and sgolayfilt(x, 3, 5), the best cubic estimated from 5 points:

          [b, a] = butter (5, 1/3);
          x = [zeros(1,15), 10*ones(1,10), zeros(1,15)];
          plot (sgolayfilt (x), "r;sgolayfilt;", ...
                filtfilt (ones (1,5)/5, 1, x), "g;5 sample average;", ...
                filtfilt (b, a, x), "c;order 5 butterworth;", ...
                x, "+b;original data;");

     See also: sgolay.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Smooth the data in x with a Savitsky-Golay smoothing filter of
polynomial order 



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
shanwavf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 100
 -- Function File: [PSI, X] = shanwavf (LB, UB, N, FB, FC)
     Compute the Complex Shannon wavelet.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Compute the Complex Shannon wavelet.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
sigmoid_train


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 556
 -- Function File: Y = sigmoid_train (T, RANGES, RC)

     Evaluate a train of sigmoid functions at T.

     The number and duration of each sigmoid is determined from RANGES.
     Each row of RANGES represents a real interval, e.g.  if sigmoid 'i'
     starts at 't=0.1' and ends at 't=0.5', then 'RANGES(i,:) = [0.1
     0.5]'.  The input RC is an array that defines the rising and
     falling time constants of each sigmoid.  Its size must equal the
     size of RANGES.

     Run 'demo sigmoid_train' to some examples of the use of this
     function.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Evaluate a train of sigmoid functions at T.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
sos2tf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 909
 -- Function File: [B, A] = sos2tf (SOS)
 -- Function File: [B, A] = sos2tf (SOS, G)
     Convert series second-order sections to direct form H(z) =
     B(z)/A(z).

     INPUTS:

        * SOS = matrix of series second-order sections, one per row:
               SOS = [B1.' A1.'; ...; BN.' AN.']
          where 'B1.' = [b0 b1 b2] and A1.' = [1 a1 a2]' for section 1,
          etc.  The b0 entry must be nonzero for each section.  See
          'filter' for documentation of the second-order direct-form
          filter coefficients Bi and Ai.

        * G is an overall gain factor that effectively scales the output
          B vector (or any one of the input Bi vectors).  If not given
          the gain is assumed to be 1.

     RETURNED: B and A are vectors specifying the digital filter H(z) =
     B(z)/A(z).  See 'filter' for further details.

     See also: tf2sos, zp2sos, sos2pz, zp2tf, tf2zp.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 69
Convert series second-order sections to direct form H(z) = B(z)/A(z).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
sos2zp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1145
 -- Function File: [Z, P, K] = sos2zp (SOS)
 -- Function File: [Z, P, K] = sos2zp (SOS, G)
     Convert series second-order sections to zeros, poles, and gains
     (pole residues).

     INPUTS:

        * SOS = matrix of series second-order sections, one per row:
               SOS = [B1.' A1.'; ...; BN.' AN.']
          where 'B1.' = [b0 b1 b2] and A1.' = [1 a1 a2]' for section 1,
          etc.  The b0 entry must be nonzero for each section.  See
          'filter' for documentation of the second-order direct-form
          filter coefficients Bi and Ai.

        * G is an overall gain factor that effectively scales any one of
          the input Bi vectors.  If not given the gain is assumed to be
          1.

     RETURNED:
        * Z = column-vector containing all zeros (roots of B(z))
        * P = column-vector containing all poles (roots of A(z))
        * K = overall gain = B(Inf)

     EXAMPLE:
          [z, p, k] = sos2zp ([1 0 1, 1 0 -0.81; 1 0 0, 1 0 0.49])
              => z = [i; -i; 0; 0]
              => p = [0.9, -0.9, 0.7i, -0.7i]
              => k = 1

     See also: zp2sos, sos2tf, tf2sos, zp2tf, tf2zp.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Convert series second-order sections to zeros, poles, and gains (pole
residues).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
specgram


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5195
 -- Function File: specgram (X)
 -- Function File: specgram (X, N)
 -- Function File: specgram (X, N, FS)
 -- Function File: specgram (X, N, FS, WINDOW)
 -- Function File: specgram (X, N, FS, WINDOW, OVERLAP)
 -- Function File: [S, F, T] = specgram (...)

     Generate a spectrogram for the signal X.  The signal is chopped
     into overlapping segments of length N, and each segment is windowed
     and transformed into the frequency domain using the FFT. The
     default segment size is 256.  If FS is given, it specifies the
     sampling rate of the input signal.  The argument WINDOW specifies
     an alternate window to apply rather than the default of 'hanning
     (N)'.  The argument OVERLAP specifies the number of samples overlap
     between successive segments of the input signal.  The default
     overlap is 'length (WINDOW)/2'.

     If no output arguments are given, the spectrogram is displayed.
     Otherwise, S is the complex output of the FFT, one row per slice, F
     is the frequency indices corresponding to the rows of S, and T is
     the time indices corresponding to the columns of S.

     Example:
             x = chirp([0:0.001:2],0,2,500);  # freq. sweep from 0-500 over 2 sec.
             Fs=1000;                  # sampled every 0.001 sec so rate is 1 kHz
             step=ceil(20*Fs/1000);    # one spectral slice every 20 ms
             window=ceil(100*Fs/1000); # 100 ms data window
             specgram(x, 2^nextpow2(window), Fs, window, window-step);

             ## Speech spectrogram
             [x, Fs] = auload(file_in_loadpath("sample.wav")); # audio file
             step = fix(5*Fs/1000);     # one spectral slice every 5 ms
             window = fix(40*Fs/1000);  # 40 ms data window
             fftn = 2^nextpow2(window); # next highest power of 2
             [S, f, t] = specgram(x, fftn, Fs, window, window-step);
             S = abs(S(2:fftn*4000/Fs,:)); # magnitude in range 0<f<=4000 Hz.
             S = S/max(S(:));           # normalize magnitude so that max is 0 dB.
             S = max(S, 10^(-40/10));   # clip below -40 dB.
             S = min(S, 10^(-3/10));    # clip above -3 dB.
             imagesc (t, f, log(S));    # display in log scale
             set (gca, "ydir", "normal"); # put the 'y' direction in the correct direction

     The choice of window defines the time-frequency resolution.  In
     speech for example, a wide window shows more harmonic detail while
     a narrow window averages over the harmonic detail and shows more
     formant structure.  The shape of the window is not so critical so
     long as it goes gradually to zero on the ends.

     Step size (which is window length minus overlap) controls the
     horizontal scale of the spectrogram.  Decrease it to stretch, or
     increase it to compress.  Increasing step size will reduce time
     resolution, but decreasing it will not improve it much beyond the
     limits imposed by the window size (you do gain a little bit,
     depending on the shape of your window, as the peak of the window
     slides over peaks in the signal energy).  The range 1-5 msec is
     good for speech.

     FFT length controls the vertical scale.  Selecting an FFT length
     greater than the window length does not add any information to the
     spectrum, but it is a good way to interpolate between frequency
     points which can make for prettier spectrograms.

     After you have generated the spectral slices, there are a number of
     decisions for displaying them.  First the phase information is
     discarded and the energy normalized:

     S = abs(S); S = S/max(S(:));

     Then the dynamic range of the signal is chosen.  Since information
     in speech is well above the noise floor, it makes sense to
     eliminate any dynamic range at the bottom end.  This is done by
     taking the max of the magnitude and some minimum energy such as
     minE=-40dB. Similarly, there is not much information in the very
     top of the range, so clipping to a maximum energy such as maxE=-3dB
     makes sense:

     S = max(S, 10^(minE/10)); S = min(S, 10^(maxE/10));

     The frequency range of the FFT is from 0 to the Nyquist frequency
     of one half the sampling rate.  If the signal of interest is band
     limited, you do not need to display the entire frequency range.  In
     speech for example, most of the signal is below 4 kHz, so there is
     no reason to display up to the Nyquist frequency of 10 kHz for a 20
     kHz sampling rate.  In this case you will want to keep only the
     first 40% of the rows of the returned S and f.  More generally, to
     display the frequency range [minF, maxF], you could use the
     following row index:

     idx = (f >= minF & f <= maxF);

     Then there is the choice of colormap.  A brightness varying
     colormap such as copper or bone gives good shape to the ridges and
     valleys.  A hue varying colormap such as jet or hsv gives an
     indication of the steepness of the slopes.  The final spectrogram
     is displayed in log energy scale and by convention has low
     frequencies on the bottom of the image:

     imagesc(t, f, flipud(log(S(idx,:))));


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Generate a spectrogram for the signal X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
square


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 379
 -- Function File: S = square (T, DUTY)
 -- Function File: S = square (T)
     Generate a square wave of period 2 pi with limits +1/-1.

     If DUTY is specified, the square wave is +1 for that portion of the
     time.

                         on time
        duty cycle = ------------------
                     on time + off time

     See also: cos, sawtooth, sin, tripuls.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
Generate a square wave of period 2 pi with limits +1/-1.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
ss2tf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 351
 -- Function File: [NUM, DEN] = ss2tf (A, B, C, D)
     Conversion from transfer function to state-space.  The state space
     system:
                .
                x = Ax + Bu
                y = Cx + Du

     is converted to a transfer function:
                          num(s)
                    G(s)=-------
                          den(s)


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Conversion from transfer function to state-space.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
ss2zp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 165
 -- Function File: [P, Z, K] = ss2zp (A, B, C, D)
     Converts a state space representation to a set of poles and zeros;
     K is a gain associated with the zeros.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Converts a state space representation to a set of poles and zeros; K is
a gain a



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
tf2sos


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1288
 -- Function File: [SOS, G] = tf2sos (B, A)
 -- Function File: SOS = tf2sos (B, A)
     Convert direct-form filter coefficients to series second-order
     sections.

     INPUTS:

     B and A are vectors specifying the digital filter H(z) = B(z)/A(z).
     See 'filter' for documentation of the B and A filter coefficients.

     RETURNED:
        * SOS = matrix of series second-order sections, one per row:
               SOS = [B1.' A1.'; ...; BN.' AN.']
          where 'B1.' = [b0 b1 b2] and A1.' = [1 a1 a2]' for section 1,
          etc.  The b0 entry must be nonzero for each section (zeros at
          infinity not supported).
        * G is an overall gain factor that effectively scales any one of
          the Bi vectors.

     If called with only one output argument, the overall filter gain is
     applied to the first second-order section in the matrix SOS.

     EXAMPLE:
          B = [1 0 0 0 0 1];
          A = [1 0 0 0 0 .9];
          [sos, g] = tf2sos (B, A)

          sos =

             1.00000   0.61803   1.00000   1.00000   0.60515   0.95873
             1.00000  -1.61803   1.00000   1.00000  -1.58430   0.95873
             1.00000   1.00000  -0.00000   1.00000   0.97915  -0.00000

          g = 1

     See also: sos2tf, zp2sos, sos2pz, zp2tf, tf2zp.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
Convert direct-form filter coefficients to series second-order sections.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
tf2ss


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 516
 -- Function File: [A, B, C, D] = tf2ss (NUM, DEN)
     Conversion from transfer function to state-space.  The state space
     system:
                .
                x = Ax + Bu
                y = Cx + Du
     is obtained from a transfer function:
                          num(s)
                    G(s)=-------
                          den(s)

     The state space system matrices obtained from this function will be
     in observable companion form as Wolovich's Observable Structure
     Theorem is used.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Conversion from transfer function to state-space.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
tf2zp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
 -- Function File: [Z, P, K] = tf2zp (NUM, DEN)
     Convert transfer functions to poles-and-zero representations.

     Returns the zeros and poles of the system defined by NUM/DEN.  K is
     a gain associated with the system zeros.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Convert transfer functions to poles-and-zero representations.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
tfe


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 381
 Usage:
   [Pxx,freq] = tfe(x,y,Nfft,Fs,window,overlap,range,plot_type,detrend)

     Estimate transfer function of system with input "x" and output "y".
     Use the Welch (1967) periodogram/FFT method.
     Compatible with Matlab R11 tfe and earlier.
     See "help pwelch" for description of arguments, hints and references
     --- especially hint (7) for Matlab R11 defaults.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 79
 Usage:
   [Pxx,freq] = tfe(x,y,Nfft,Fs,window,overlap,range,plot_type,detrend)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
tfestimate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 524
 -- Function File: tfestimate (X, Y)
 -- Function File: tfestimate (X, Y, WINDOW)
 -- Function File: tfestimate (X, Y, WINDOW, OVERLAP)
 -- Function File: tfestimate (X, Y, WINDOW, OVERLAP, NFFT)
 -- Function File: tfestimate (X, Y, WINDOW, OVERLAP, NFFT, FS)
 -- Function File: tfestimate (X, Y, WINDOW, OVERLAP, NFFT, FS, RANGE)
 -- Function File: [PXX, FREQ] = tfestimate (...)

     Estimate transfer function of system with input X and output Y.
     Use the Welch (1967) periodogram/FFT method.

     See also: pwelch.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 63
Estimate transfer function of system with input X and output Y.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
triang


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 333
 -- Function File: triang (M)

     Return the filter coefficients of a triangular window of length M.
     Unlike the Bartlett window, 'triang' does not go to zero at the
     edges of the window.  For odd M, 'triang (M)' is equal to 'bartlett
     (M + 2)' except for the zeros at the edges of the window.

     See also: bartlett.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Return the filter coefficients of a triangular window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
tripuls


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 775
 -- Function File: Y = tripuls (T)
 -- Function File: Y = tripuls (T, W)
 -- Function File: Y = tripuls (T, W, SKEW)

     Generate a triangular pulse over the interval [-w/2,w/2), sampled
     at times t.  This is useful with the function pulstran for
     generating a series pulses.

     skew is a value between -1 and 1, indicating the relative placement
     of the peak within the width.  -1 indicates that the peak should be
     at -w/2, and 1 indicates that the peak should be at w/2.

     Example:
          fs = 11025;  # arbitrary sample rate
          f0 = 100;    # pulse train sample rate
          w = 0.3/f0;  # pulse width 3/10th the distance between pulses
          auplot(pulstran(0:1/fs:4/f0, 0:1/f0:4/f0, 'tripuls', w), fs);

     See also: pulstran.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 77
Generate a triangular pulse over the interval [-w/2,w/2), sampled at
times t.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
tukeywin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 706
 -- Function File: tukeywin (M)
 -- Function File: tukeywin (M, R)
     Return the filter coefficients of a Tukey window (also known as the
     cosine-tapered window) of length M.  R defines the ratio between
     the constant section and and the cosine section.  It has to be
     between 0 and 1.  The function returns a Hanning window for R equal
     to 0 and a full box for R equals to 1.  The default value of R is
     1/2.

     For a definition of the Tukey window, see e.g.  Fredric J. Harris,
     "On the Use of Windows for Harmonic Analysis with the Discrete
     Fourier Transform, Proceedings of the IEEE", Vol.  66, No.  1,
     January 1978, Page 67, Equation 38.

     See also: hanning.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return the filter coefficients of a Tukey window (also known as the
cosine-taper



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
ultrwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2413
 -- Function File: [W, XMU] = ultrwin (M, MU, BETA)
 -- Function File: [W, XMU] = ultrwin (M, MU, ATT, "att")
 -- Function File: [W, XMU] = ultrwin (M, MU, LATT, "latt")
 -- Function File: W = ultrwin (M, MU, XMU, "xmu")
     Return the coefficients of an Ultraspherical window of length M.
     The parameter MU controls the window's Fourier transform's
     side-lobe to side-lobe ratio, and the third given parameter
     controls the transform's main-lobe width/side-lobe-ratio; normalize
     W such that the central coefficient(s) value is unitary.

     By default, the third parameter is BETA, which sets the main lobe
     width to BETA times that of a rectangular window.  Alternatively,
     giving ATT or LATT sets the ripple ratio at the first or last
     side-lobe respectively, or giving XMU sets the (un-normalized)
     window's Fourier transform according to its canonical definition:

                  (MU)
          W(k) = C   [ XMU cos(pi k/M) ],  k = 0, 1, ..., M-1,
                  M-1

     where C is the Ultraspherical (a.k.a.  Gegenbauer) polynomial,
     which can be defined using the recurrence relationship:

           (l)    1                  (l)                    (l)
          C (x) = - [ 2x(m + l - 1) C   (x) - (m + 2l - 2) C   (x) ]
           m      m                  m-1                    m-2

                                     (l)        (l)
          for m an integer > 1, and C (x) = 1, C (x) = 2lx.
                                     0          1

     For given BETA, ATT, or LATT, the corresponding (determined) value
     of XMU is also returned.

     The Dolph-Chebyshev and Saramaki windows are special cases of the
     Ultraspherical window, with MU set to 0 and 1 respectively.  Note
     that when not giving XMU, stability issues may occur with MU <=
     -1.5.  For further information about the window, see

        * Kabal, P., 2009: Time Windows for Linear Prediction of Speech.
          Technical Report, Dept.  Elec.  & Comp.  Eng., McGill
          University.
        * Bergen, S., Antoniou, A., 2004: Design of Ultraspherical
          Window Functions with Prescribed Spectral Characteristics.
          Proc.  JASP, 13/13, pp.  2053-2065.
        * Streit, R., 1984: A two-parameter family of weights for
          nonrecursive digital filters and antennas.  Trans.  ASSP, 32,
          pp.  108-118.

     See also: chebwin, kaiser.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Return the coefficients of an Ultraspherical window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
upsample


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 370
 -- Function File: Y = upsample (X, N)
 -- Function File: Y = upsample (X, N, OFFSET)
     Upsample the signal, inserting N-1 zeros between every element.

     If X is a matrix, upsample every column.

     If OFFSET is specified, control the position of the inserted sample
     in the block of N zeros.

     See also: decimate, downsample, interp, resample, upfirdn.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 63
Upsample the signal, inserting N-1 zeros between every element.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
upsamplefill


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 773
 -- Function File: Y = upsamplefill (X, V)
 -- Function File: Y = upsamplefill (..., COPY)
     Upsamples a vector interleaving given values or copies of the
     vector elements.

     The values in the vector V are placed between the elements of X.

     If the optional argument COPY is TRUE then V should be a scalar and
     each value in X are repeat V times.

     Example:
          upsamplefill (eye (2), 2, true)
          =>  1   0
              1   0
              1   0
              0   1
              0   1
              0   1
          upsamplefill (eye (2), [-1 -1 -1])
          =>  1   0
             -1  -1
             -1  -1
             -1  -1
              0   1
             -1  -1
             -1  -1
             -1  -1

     See also: upsample.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 78
Upsamples a vector interleaving given values or copies of the vector
elements.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
wconv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 342
 -- Function File: Y = wconv (TYPE, X, F)
 -- Function File: Y = wconv (TYPE, X, F, SHAPE)
     1-D or 2-D convolution.

     *Inputs*
     TYPE
          Type of convolution.
     X
          Signal vector or matrix.
     F
          Coefficients of FIR filter.
     SHAPE
          Shape.

     *Outputs*
     Y
          Convoluted signal.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
1-D or 2-D convolution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
welchwin


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 794
 -- Function File: welchwin (M)
 -- Function File: welchwin (M, "periodic")
 -- Function File: welchwin (M, "symmetric")
     Return the filter coefficients of a Welch window of length M.  The
     Welch window is given by W(n)=1-(n/N-1)^2, n=[0,1, ...  M-1].  The
     optional argument specifies a "symmetric" window (the default) or a
     "periodic" window.

     A symmetric window has zero at each end and maximum in the middle,
     and the length must be an integer greater than 2.  The variable N
     in the formula above is '(M-1)/2'.

     A periodic window wraps around the cyclic interval [0,1, ...  M-1],
     and is intended for use with the DFT. The length must be an integer
     greater than 1.  The variable N in the formula above is 'M/2'.

     See also: blackman, kaiser.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Return the filter coefficients of a Welch window of length M.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
window


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 256
 -- Function File: W = window (F, M)
 -- Function File: W = window (F, M, OPTS)
     Create an M-point window from the function F.  The function F can
     be for example '@blackman'.  Any additional arguments OPT are
     passed to the windowing function.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
Create an M-point window from the function F.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
wkeep


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 162
 -- Function File: Y = wkeep (X, L)
 -- Function File: Y = wkeep (X, L, OPT)
     Extract the elements of X of size L from the center, the right or
     the left.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 75
Extract the elements of X of size L from the center, the right or the
left.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
wrev


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 118
 -- Function File: Y = wrev (X)
     Reverse the order of the element of the vector X.

     See also: flipud, fliplr.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Reverse the order of the element of the vector X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
xcorr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3021
 -- Function File: [R, LAG] = xcorr ( X )
 -- Function File: ... = xcorr ( X, Y )
 -- Function File: ... = xcorr ( ..., MAXLAG)
 -- Function File: ... = xcorr ( ..., SCALE)
     Estimates the cross-correlation.

     Estimate the cross correlation R_xy(k) of vector arguments X and Y
     or, if Y is omitted, estimate autocorrelation R_xx(k) of vector X,
     for a range of lags k specified by argument "maxlag".  If X is a
     matrix, each column of X is correlated with itself and every other
     column.

     The cross-correlation estimate between vectors "x" and "y" (of
     length N) for lag "k" is given by

                     N
          R_xy(k) = sum x_{i+k} conj(y_i),
                    i=1

     where data not provided (for example x(-1), y(N+1)) is zero.  Note
     the definition of cross-correlation given above.  To compute a
     cross-correlation consistent with the field of statistics, see
     'xcov'.

     *ARGUMENTS*
     X
          [non-empty; real or complex; vector or matrix] data

     Y
          [real or complex vector] data

          If X is a matrix (not a vector), Y must be omitted.  Y may be
          omitted if X is a vector; in this case xcorr estimates the
          autocorrelation of X.

     MAXLAG
          [integer scalar] maximum correlation lag If omitted, the
          default value is N-1, where N is the greater of the lengths of
          X and Y or, if X is a matrix, the number of rows in X.

     SCALE
          [character string] specifies the type of scaling applied to
          the correlation vector (or matrix).  is one of:
          'none'
               return the unscaled correlation, R,
          'biased'
               return the biased average, R/N,
          'unbiased'
               return the unbiased average, R(k)/(N-|k|),
          'coeff'
               return the correlation coefficient, R/(rms(x).rms(y)),
               where "k" is the lag, and "N" is the length of X.  If
               omitted, the default value is "none".  If Y is supplied
               but does not have the same length as X, scale must be
               "none".

     *RETURNED VARIABLES*
     R
          array of correlation estimates
     LAG
          row vector of correlation lags [-maxlag:maxlag]

     The array of correlation estimates has one of the following forms:
     (1) Cross-correlation estimate if X and Y are vectors.

     (2) Autocorrelation estimate if is a vector and Y is omitted.

     (3) If X is a matrix, R is an matrix containing the
     cross-correlation estimate of each column with every other column.
     Lag varies with the first index so that R has 2*maxlag+1 rows and
     P^2 columns where P is the number of columns in X.

     If Rij(k) is the correlation between columns i and j of X

     'R(k+maxlag+1,P*(i-1)+j) == Rij(k)'

     for lag k in [-maxlag:maxlag], or

     'R(:,P*(i-1)+j) == xcorr(X(:,i),X(:,j))'.

     'reshape(R(k,:),P,P)' is the cross-correlation matrix for 'X(k,:)'.

     See also: xcov.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
Estimates the cross-correlation.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
xcorr2


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1009
 -- Function File: xcorr2 (A)
 -- Function File: xcorr2 (A, B)
 -- Function File: xcorr2 (..., SCALE)
     Compute the 2D cross-correlation of matrices A and B.

     If B is not specified, computes autocorrelation of A, i.e., same as
     'xcorr (A, A)'.

     The optional argument SCALE, defines the type of scaling applied to
     the cross-correlation matrix.  Possible values are:

     "none" (default)
          No scaling.

     "biased"
          Scales the raw cross-correlation by the maximum number of
          elements of A and B involved in the generation of any element
          of C.

     "unbiased"
          Scales the raw correlation by dividing each element in the
          cross-correlation matrix by the number of products A and B
          used to generate that element.

     "coeff"
          Scales the normalized cross-correlation on the range of [0 1]
          so that a value of 1 corresponds to a correlation coefficient
          of 1.

     See also: conv2, corr2, xcorr.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
Compute the 2D cross-correlation of matrices A and B.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
xcov


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 938
 -- Function File: [R, LAG] = xcov ( X )
 -- Function File: ... = xcov ( X, Y )
 -- Function File: ... = xcov ( ..., MAXLAG)
 -- Function File: ... = xcov ( ..., SCALE)
     Compute covariance at various lags
     [=correlation(x-mean(x),y-mean(y))].

     X
          input vector
     Y
          if specified, compute cross-covariance between X and Y,
          otherwise compute autocovariance of X.
     MAXLAG
          is specified, use lag range [-maxlag:maxlag], otherwise use
          range [-n+1:n-1].
     SCALE:
          'biased'
               for covariance=raw/N,
          'unbiased'
               for covariance=raw/(N-|lag|),
          'coeff'
               for covariance=raw/(covariance at lag 0),
          'none'
               for covariance=raw
          'none'
               is the default.

     Returns the covariance for each lag in the range, plus an optional
     vector of lags.

     See also: xcorr.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 71
Compute covariance at various lags [=correlation(x-mean(x),y-mean(y))].



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
zerocrossing


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 184
 -- Function File: X0 = zerocrossing (X, Y)
     Estimates the points at which a given waveform y=y(x) crosses the
     x-axis using linear interpolation.

     See also: fzero, roots.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Estimates the points at which a given waveform y=y(x) crosses the x-axis
using l



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
zp2sos


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1513
 -- Function File: [SOS, G] = zp2sos (Z)
 -- Function File: [SOS, G] = zp2sos (Z, P)
 -- Function File: [SOS, G] = zp2sos (Z, P, K)
 -- Function File: SOS = zp2sos (...)
     Convert filter poles and zeros to second-order sections.

     INPUTS:
        * Z = column-vector containing the filter zeros
        * P = column-vector containing the filter poles
        * K = overall filter gain factor If not given the gain is
          assumed to be 1.

     RETURNED:
        * SOS = matrix of series second-order sections, one per row:
               SOS = [B1.' A1.'; ...; BN.' AN.']
          where 'B1.' = [b0 b1 b2] and A1.' = [1 a1 a2]' for section 1,
          etc.  The b0 entry must be nonzero for each section.  See
          'filter' for documentation of the second-order direct-form
          filter coefficients Bi and %Ai, i=1:N.

        * G is the overall gain factor that effectively scales any one
          of the Bi vectors.

     If called with only one output argument, the overall filter gain is
     applied to the first second-order section in the matrix SOS.

     EXAMPLE:
            [z, p, k] = tf2zp ([1 0 0 0 0 1], [1 0 0 0 0 .9]);
            [sos, g] = zp2sos (z, p, k)

          sos =
             1.0000    0.6180    1.0000    1.0000    0.6051    0.9587
             1.0000   -1.6180    1.0000    1.0000   -1.5843    0.9587
             1.0000    1.0000         0    1.0000    0.9791         0

          g =
              1

     See also: sos2pz, sos2tf, tf2sos, zp2tf, tf2zp.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
Convert filter poles and zeros to second-order sections.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
zp2ss


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 549
 -- Function File: [A, B, C, D] = zp2ss (Z, P, K)
     Conversion from zero / pole to state space.

     *Inputs*
     Z
     P
          Vectors of (possibly) complex poles and zeros of a transfer
          function.  Complex values must come in conjugate pairs (i.e.,
          x+jy in Z means that x-jy is also in Z).
     K
          Real scalar (leading coefficient).

     *Outputs*
     A
     B
     C
     D
          The state space system, in the form:
                    .
                    x = Ax + Bu
                    y = Cx + Du


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Conversion from zero / pole to state space.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
zp2tf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 318
 -- Function File: [NUM, DEN] = zp2tf (Z, P, K)
     Converts zeros / poles to a transfer function.

     *Inputs*
     Z
     P
          Vectors of (possibly complex) poles and zeros of a transfer
          function.  Complex values must appear in conjugate pairs.
     K
          Real scalar (leading coefficient).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Converts zeros / poles to a transfer function.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
zplane


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1330
 -- Function File: zplane (Z, P)
 -- Function File: zplane (B, A)

     Plot the poles and zeros.  If the arguments are row vectors then
     they represent filter coefficients (numerator polynomial b and
     denominator polynomial a), but if they are column vectors or
     matrices then they represent poles and zeros.

     This is a horrid interface, but I didn't choose it; better would be
     to accept b,a or z,p,g like other functions.  The saving grace is
     that poly(x) always returns a row vector and roots(x) always
     returns a column vector, so it is usually right.  You must only be
     careful when you are creating filters by hand.

     Note that due to the nature of the roots() function, poles and
     zeros may be displayed as occurring around a circle rather than at
     a single point.

     The transfer function is

                 B(z)   b0 + b1 z^(-1) + b2 z^(-2) + ... + bM z^(-M)
          H(z) = ---- = --------------------------------------------
                 A(z)   a0 + a1 z^(-1) + a2 z^(-2) + ... + aN z^(-N)

                        b0          (z - z1) (z - z2) ... (z - zM)
                      = -- z^(-M+N) ------------------------------
                        a0          (z - p1) (z - p2) ... (z - pN)

     The denominator a defaults to 1, and the poles p defaults to [].


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Plot the poles and zeros.