Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / aryule.m

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+## 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')