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view main/signal/levinson.m @ 0:6b33357c7561 octave-forge
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author | pkienzle |
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date | Wed, 10 Oct 2001 19:54:49 +0000 |
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children | e26254f9e5dc |
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## Copyright (C) 1999 Paul Kienzle ## ## 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 2 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, write to the Free Software ## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA ## ## Based on: ## yulewalker.m ## Copyright (C) 1995 (GPL) ## Friedrich Leisch <Friedrich.Leisch@ci.tuwien.ac.at> ## 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. ## Author: PAK <pkienzle@kienzle.powernet.co.uk> ## 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( columns (acf) > 1 ) acf=acf'; endif if (nargin == 1) p = length(acf) - 1; endif if nargout < 3 && p < 100 ## direct solution [O(p^3), but no loops so slightly faster for small p] R = toeplitz(acf(1:p), conj(acf(1:p))); a = R \ -acf(2:p+1); a = [ 1, a' ]; v = sum(a'.*acf(1:p+1)); else ## durbin-levinson [O(p^2), so significantly faster for large p] ref = zeros (1, p); g = acf(2) / acf(1); a = [ g ]; v = ( 1 - g^2 ) * acf(1); ref(1) = g; for t = 2 : p g = (acf(t+1) - a * acf(2:t)) / v; a = [ g, a-g*a(t-1:-1:1) ]; v = v * ( 1 - g^2 ) ; ref(t) = g; endfor a = [1, -a(p:-1:1)]; endif endfunction