Add a useful package (from Source forge) for octave

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

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+## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
+## Copyright (C) 2006 Peter V. Lanspeary, <peter.lanspeary@.adelaide.edu.au>
+##
+## 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, ref] = 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
+
+## Based on:
+##    yulewalker.m
+##    Copyright (C) 1995 Friedrich Leisch <Friedrich.Leisch@ci.tuwien.ac.at>
+##    GPL license
+
+## TODO: Matlab doesn't return reflection coefficients and 
+## TODO:    errors in addition to the polynomial a.
+## TODO: What is the difference between aryule, levinson, 
+## TODO:    ac2poly, ac2ar, lpc, etc.?
+
+function [a, v, ref] = levinson (acf, p)
+  if ( nargin<1 )
+    print_usage;
+  elseif( ~isvector(acf) || length(acf)<2 )
+    error( "levinson: arg 1 (acf) must be vector of length >1\n");
+  elseif ( nargin>1 && ( ~isscalar(p) || fix(p)~=p ) )
+    error( "levinson: arg 2 (p) must be integer >0\n");
+  else
+    if ((nargin == 1)||(p>=length(acf))) p = length(acf) - 1; endif
+    if( columns(acf)>1 ) acf=acf(:); endif      # force a column vector
+
+    if nargout < 3 && p < 100
+      ## direct solution [O(p^3), but no loops so slightly faster for small p]
+      ##   Kay & Marple Eqn (2.39)
+      R = toeplitz(acf(1:p), conj(acf(1:p)));
+      a = R \ -acf(2:p+1);
+      a = [ 1, a.' ];
+      v = real( a*conj(acf(1:p+1)) );
+    else
+      ## durbin-levinson [O(p^2), so significantly faster for large p]
+      ##   Kay & Marple Eqns (2.42-2.46)
+      ref = zeros(p,1);
+      g = -acf(2)/acf(1);
+      a = [ g ];
+      v = real( ( 1 - g*conj(g)) * acf(1) );
+      ref(1) = g;
+      for t = 2 : p
+        g = -(acf(t+1) + a * acf(t:-1:2)) / v;
+        a = [ a+g*conj(a(t-1:-1:1)), g ];
+        v = v * ( 1 - real(g*conj(g)) ) ;
+        ref(t) = g;
+      endfor
+      a = [1, a];
+    endif
+  endif
+endfunction