--- /dev/null
+## 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