This file is indexed.

/usr/share/octave/packages/signal-1.3.2/ultrwin.m is in octave-signal 1.3.2-5.

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
## Copyright (c) 2013 Rob Sykes <robs@users.sourceforge.net>
##
## This program is free software: you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation, either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn  {Function File} {[@var{w}, @var{xmu}] =} ultrwin (@var{m}, @var{mu}, @var{beta})
## @deftypefnx {Function File} {[@var{w}, @var{xmu}] =} ultrwin (@var{m}, @var{mu}, @var{att}, "att")
## @deftypefnx {Function File} {[@var{w}, @var{xmu}] =} ultrwin (@var{m}, @var{mu}, @var{latt}, "latt")
## @deftypefnx {Function File} {@var{w} =} ultrwin (@var{m}, @var{mu}, @var{xmu}, "xmu")
## Return the coefficients of an Ultraspherical window of length @var{m}.
## The parameter @var{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 @var{w} such that the central
## coefficient(s) value is unitary.
##
## By default, the third parameter is @var{beta}, which sets the main lobe width
## to @var{beta} times that of a rectangular window.  Alternatively, giving
## @var{att} or @var{latt} sets the ripple ratio at the first or last side-lobe
## respectively, or giving @var{xmu} sets the (un-normalized) window's Fourier
## transform according to its canonical definition:
##
## @verbatim
##              (MU)
##      W(k) = C   [ XMU cos(pi k/M) ],  k = 0, 1, ..., M-1,
##              M-1
## @end verbatim
##
## where C is the Ultraspherical (a.k.a. Gegenbauer) polynomial, which can be
## defined using the recurrence relationship:
##
## @verbatim
##       (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
## @end verbatim
##
## For given @var{beta}, @var{att}, or @var{latt}, the corresponding
## (determined) value of @var{xmu} is also returned.
##
## The Dolph-Chebyshev and Saramaki windows are special cases of the
## Ultraspherical window, with @var{mu} set to 0 and 1 respectively.  Note that
## when not giving @var{xmu}, stability issues may occur with @var{mu} <= -1.5.
## For further information about the window, see
##
## @itemize @bullet
## @item
## Kabal, P., 2009: Time Windows for Linear Prediction of Speech.
## Technical Report, Dept. Elec. & Comp. Eng., McGill University.
## @item
## Bergen, S., Antoniou, A., 2004: Design of Ultraspherical Window
## Functions with Prescribed Spectral Characteristics. Proc. JASP, 13/13,
## pp. 2053-2065.
## @item
## Streit, R., 1984: A two-parameter family of weights for nonrecursive
## digital filters and antennas. Trans. ASSP, 32, pp. 108-118.
## @end itemize
## @seealso{chebwin, kaiser}
## @end deftypefn

function [w, xmu] = ultrwin (m, mu, par, key = "beta", norm = 0)
  ## This list of parameter types must be kept in sync with the enum order.
  types = {"xmu", "beta", "att", "latt"};
  type = [];
  if (ischar (key))
    type = find (strncmpi (key, types, numel (key)));
  endif

  if (nargin < 3 || nargin > 5)
    print_usage ();
  elseif (! (isscalar (m) && (m == fix (m)) && (m > 0)))
    error ("ultrwin: M must be a positive integer");
  elseif (! (isscalar (mu) && isreal (mu)))
    error ("ultrwin: MU must be a real scalar");
  elseif (! ischar (key))
    error ("ultrwin: parameter type must be a string");
  elseif (isempty (type))
    error ("ultrwin: invalid parameter type '%s'", key);
  elseif (! (isscalar (par) && isreal (par)))
    error (["ultrwin: ", upper (types(type)), " must be a real scalar"]);
  elseif (! (isscalar (norm) && norm == fix (norm) && norm >= 0)) # Alt. norms; WIP
    error ("ultrwin: NORM must be a non-negative integer");
  endif

  [w, xmu] = __ultrwin__(m, mu, par, type-1, norm);

endfunction

%!test
%! assert(ultrwin(100, 1, 1), ones(100, 1), 1e-14);

%!test
%! L = 201; xmu = 1.01; m = L-1;
%! for mu = -1.35:.3:1.35
%!   x = xmu*cos([0:m]*pi/L);
%!   C(2,:) = 2*mu*x; C(1,:) = 1;
%!   for k = 2:m; C(k+1,:) = 2*(k+mu-1)/k*x.*C(k,:) - (k+2*mu-2)/k*C(k-1,:); end
%!   b = real(ifft(C(m+1,:))); b = b(m/2+2:L)/b(1);
%!   assert(ultrwin(L, mu, xmu, "x")', [b 1 fliplr(b)], 1e-12);
%! end

%!test
%! b = [
%!   5.7962919401511820e-03
%!   1.6086991349967078e-02
%!   3.6019014684117417e-02
%!   6.8897525451558125e-02
%!   1.1802364384553447e-01
%!   1.8566749737411145e-01
%!   2.7234740630826737e-01
%!   3.7625460141456091e-01
%!   4.9297108901880221e-01
%!   6.1558961695849457e-01
%!   7.3527571856983598e-01
%!   8.4222550739092694e-01
%!   9.2688779484512085e-01
%!   9.8125497127708561e-01]';
%! [w xmu] = ultrwin(29, 0, 3);
%! assert(w', [b 1 fliplr(b)], 1e-14);
%! assert(xmu, 1.053578297819277, 1e-14);

%!test
%! b = [
%!   2.9953636903962466e-02
%!   7.6096450051659603e-02
%!   1.5207129867916891e-01
%!   2.5906995366355179e-01
%!   3.9341065451220536e-01
%!   5.4533014012036929e-01
%!   6.9975915071207051e-01
%!   8.3851052636906720e-01
%!   9.4345733548690369e-01]';
%! assert(ultrwin(20, .5, 50, "a")', [b 1 1 fliplr(b)], 1e-14);

%!test
%! b = [
%!   1.0159906492322712e-01
%!   1.4456358609406283e-01
%!   2.4781689516201011e-01
%!   3.7237015168857646e-01
%!   5.1296973026690407e-01
%!   6.5799041448113671e-01
%!   7.9299087042967320e-01
%!   9.0299778924260576e-01
%!   9.7496213649820296e-01]';
%! assert(ultrwin(19, -.4, 40, "l")', [b 1 fliplr(b)], 1e-14);

%!demo
%! w=ultrwin(120, -1, 40, "l"); [W,f]=freqz(w); clf
%! subplot(2,1,1); plot(f/pi, 20*log10(W/abs(W(1)))); grid; axis([0 1 -90 0])
%! subplot(2,1,2); plot(0:length(w)-1, w); grid
%! %-----------------------------------------------------------
%! % Figure shows an Ultraspherical window with MU=-1, LATT=40:
%! % frequency domain above, time domain below.

%!demo
%! c="krbm"; clf; subplot(2, 1, 1)
%! for beta=2:5
%!   w=ultrwin(80, -.5, beta); [W,f]=freqz(w);
%!   plot(f/pi, 20*log10(W/abs(W(1))), c(1+mod(beta, length(c)))); hold on
%! end; grid; axis([0 1 -140 0]); hold off
%! subplot(2, 1, 2);
%! for n=2:10
%!   w=ultrwin(n*20, 1, 3); [W,f]=freqz(w,1,2^11);
%!   plot(f/pi, 20*log10(W/abs(W(1))), c(1+mod(n, length(c)))); hold on
%! end; grid; axis([0 .2 -100 0]); hold off
%! %--------------------------------------------------
%! % Figure shows transfers of Ultraspherical windows:
%! % above: varying BETA with fixed N & MU,
%! % below: varying N with fixed MU & BETA.

%!demo
%! c="krbm"; clf; subplot(2, 1, 1)
%! for j=0:4
%!   w=ultrwin(80, j*.6-1.2, 50, "a"); [W,f]=freqz(w);
%!   plot(f/pi, 20*log10(W/abs(W(1))), c(1+mod(j, length(c)))); hold on
%! end; grid; axis([0 1 -100 0]); hold off
%! subplot(2, 1, 2);
%! for j=4:-1:0
%!   w=ultrwin(80, j*.75-1.5, 50, "l"); [W,f]=freqz(w);
%!   plot(f/pi, 20*log10(W/abs(W(1))), c(1+mod(j, length(c)))); hold on
%! end; grid; axis([0 1 -100 0]); hold off
%! %--------------------------------------------------
%! % Figure shows transfers of Ultraspherical windows:
%! % above: varying MU with fixed N & ATT,
%! % below: varying MU with fixed N & LATT.

%!demo
%! clf; a=[.8 2 -115 5]; fc=1.1/pi; l="labelxy";
%! for k=1:3; switch (k); case 1; w=kaiser(L=159, 7.91);
%!   case 2; w=ultrwin(L=165, 0, 2.73); case 3; w=ultrwin(L=153, .5, 2.6); end
%!   subplot(3, 1, 4-k); f=[1:(L-1)/2]*pi;f=sin(fc*f)./f; f=[fliplr(f) fc f]';
%!   [h,f]=freqz(w.*f,1,2^14); plot(f,20*log10(h)); grid; axis(a,l); l="labely";
%! end
%! %-----------------------------------------------------------
%! % Figure shows example lowpass filter design (Fp=1, Fs=1.2
%! % rad/s, att=80 dB) and comparison with other windows.  From
%! % top to bottom: Ultraspherical, Dolph-Chebyshev, and Kaiser
%! % windows, with lengths 153, 165, and 159 respectively.