/usr/share/octave/packages/signal-1.2.2/aryule.m is in octave-signal 1.2.2-1build1.
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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 | ## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
## Copyright (C) 2006 Peter Lanspeary
##
## 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/>.
## usage: [a, v, k] = aryule (x, p)
##
## fits an AR (p)-model with Yule-Walker estimates.
## x = data vector to estimate
## a: AR coefficients
## v: variance of white noise
## k: reflection coeffients 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.
function [a, v, k] = aryule (x, p)
if ( nargin~=2 )
print_usage;
elseif ( ~isvector(x) || length(x)<3 )
error( 'aryule: arg 1 (x) must be vector of length >2' );
elseif ( ~isscalar(p) || fix(p)~=p || p > length(x)-2 )
error( 'aryule: arg 2 (p) must be an integer >0 and <length(x)-1' );
endif
c = xcorr(x, p+1, 'biased');
c(1:p+1) = []; # remove negative autocorrelation lags
c(1) = real(c(1)); # levinson/toeplitz requires exactly c(1)==conj(c(1))
if nargout <= 1
a = levinson(c, p);
elseif nargout == 2
[a, v] = levinson(c, p);
else
[a, v, k] = levinson(c, p);
endif
endfunction
%!demo
%! % use demo('pyulear')
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