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function [MX,res,arg3] = durlev(AutoCov); % function [AR,RC,PE] = durlev(ACF); % function [MX,PE] = durlev(ACF); % estimates AR(p) model parameter by solving the % Yule-Walker with the Durbin-Levinson recursion % for multiple channels % INPUT: % ACF Autocorrelation function from lag=[0:p] % % OUTPUT % AR autoregressive model parameter % RC reflection coefficients (= -PARCOR coefficients) % PE remaining error variance % MX transformation matrix between ARP and RC (Attention: needs O(p^2) memory) % AR(:,K) = MX(:,K*(K-1)/2+(1:K)); % RC(:,K) = MX(:,(1:K).*(2:K+1)/2); % % All input and output parameters are organized in rows, one row % corresponds to the parameters of one channel % % see also ACOVF ACORF AR2RC RC2AR LATTICE % % REFERENCES: % Levinson N. (1947) "The Wiener RMS(root-mean-square) error criterion in filter design and prediction." J. Math. Phys., 25, pp.261-278. % Durbin J. (1960) "The fitting of time series models." Rev. Int. Stat. Inst. vol 28., pp 233-244. % P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991. % S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996. % M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. % W.S. Wei "Time Series Analysis" Addison Wesley, 1990. % Version 2.99 23.05.2002 % Copyright (C) 1998-2002 by Alois Schloegl <a.schloegl@ieee.org> % This library is free software; you can redistribute it and/or % modify it under the terms of the GNU Library General Public % License as published by the Free Software Foundation; either % Version 2 of the License, or (at your option) any later version. % % This library 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 % Library General Public License for more details. % % You should have received a copy of the GNU Library General Public % License along with this library; if not, write to the % Free Software Foundation, Inc., 59 Temple Place - Suite 330, % Boston, MA 02111-1307, USA. % Inititialization [lr,lc]=size(AutoCov); res=[AutoCov(:,1), zeros(lr,lc-1)]; d=zeros(lr,1); if nargout<3 % needs O(p^2) memory MX=zeros(lr,lc*(lc-1)/2); idx=0; idx1=0; % Durbin-Levinson Algorithm for K=1:lc-1, %idx=K*(K-1)/2; %see below % for L=1:lr, d(L)=arp(L,1:K-1)*transpose(AutoCov(L,K:-1:2));end; % Matlab 4.x, Octave % d=sum(MX(:,idx+(1:K-1)).*AutoCov(:,K:-1:2),2); % Matlab 5.x MX(:,idx+K)=(AutoCov(:,K+1)-sum(MX(:,idx1+(1:K-1)).*AutoCov(:,K:-1:2),2))./res(:,K); %rc(:,K)=arp(:,K); %if K>1 %for compatibility with OCTAVE 2.0.13 MX(:,idx+(1:K-1))=MX(:,idx1+(1:K-1))-MX(:,(idx+K)*ones(K-1,1)).*MX(:,idx1+(K-1:-1:1)); %end; % for L=1:lr, d(L)=MX(L,idx+(1:K))*(AutoCov(L,K+1:-1:2).');end; % Matlab 4.x, Octave % d=sum(MX(:,idx+(1:K)).*AutoCov(:,K+1:-1:2),2); % Matlab 5.x res(:,K+1) = res(:,K).*(1-abs(MX(:,idx+K)).^2); idx1=idx; idx=idx+K; end; %arp=MX(:,K*(K-1)/2+(1:K)); %rc =MX(:,(1:K).*(2:K+1)/2); else % needs O(p) memory arp=zeros(lr,lc-1); rc=zeros(lr,lc-1); % Durbin-Levinson Algorithm for K=1:lc-1, % for L=1:lr, d(L)=arp(L,1:K-1)*transpose(AutoCov(L,K:-1:2));end; % Matlab 4.x, Octave % d=sum(arp(:,1:K-1).*AutoCov(:,K:-1:2),2); % Matlab 5.x arp(:,K) = (AutoCov(:,K+1)-sum(arp(:,1:K-1).*AutoCov(:,K:-1:2),2))./res(:,K); % Yule-Walker rc(:,K) = arp(:,K); %if K>1 %for compatibility with OCTAVE 2.0.13 arp(:,1:K-1)=arp(:,1:K-1)-arp(:,K*ones(K-1,1)).*arp(:,K-1:-1:1); %end; %for L=1:lr, d(L)=arp(L,1:K)*(AutoCov(L,K+1:-1:2).');end; % Matlab 4.x, Octave % d=sum(arp(:,1:K).*AutoCov(:,K+1:-1:2),2); % Matlab 5.x res(:,K+1) = res(:,K).*(1-abs(arp(:,K)).^2); end; % assign output arguments arg3=res; res=rc; MX=arp; end; %if