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function [MX,res,arg3,acf] = rc2ar(rC); % converts reflection coefficients into autoregressive parameters % uses the Durbin-Levinson recursion for multiple channels % function [AR,RC,PE,ACF] = rc2ar(RC); % function [MX,PE] = rc2ar(RC); % % INPUT: % RC reflection coefficients % % OUTPUT % AR autoregressive model parameter % RC reflection coefficients (= -PARCOR coefficients) % PE remaining error variance (relative to PE(1)=1) % MX transformation matrix between ARP and RC (Attention: needs O(p^2) memory) % arp=MX(:,K*(K-1)/2+(1:K)); % rc =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 DURLEV AR2RC % % REFERENCES: % 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 2.90 last revision 10.04.2002 % Copyright (c) 1996-2002 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(rc); res=[ones(lr,1) zeros(lr,lc)]; if nargout<3 % needs O(p^2) memory MX=zeros(lr,lc*(lc+1)/2); idx=0; % Durbin-Levinson Algorithm for K=1:lc, MX(:,idx+K)=rc(:,K);%(AutoCov(:,K+1)-d)./res(:,K); %rc(:,K)=arp(:,K); if K>1 %for compatibility with OCTAVE 2.0.13 MX(:,idx+(1:K-1))=MX(:,(K-2)*(K-1)/2+(1:K-1))-MX(:,(idx+K)*ones(K-1,1)).*MX(:,(K-2)*(K-1)/2+(K-1:-1:1)); end; res(:,K+1) = res(:,K).*(1-abs(MX(:,idx+K)).^2); idx=idx+K; end; %arp=MX(:,K*(K-1)/2+(1:K)); %rc =MX(:,(1:K).*(2:K+1)/2); ACF=cumprod(ones(lr,lr)-rc.^2,2); else % needs O(p) memory ar=zeros(lr,lc); acf=[ones(lr,1),zeros(lr,lc)]; %rc=RC; %zeros(lr,lc-1); % Durbin-Levinson Algorithm for K=1:lc, acf(:,K) = -sum(acf(:,K:-1:1).*ar(:,1:K),2); ar(:,K) = rc(:,K); if K>1, %for compatibility with OCTAVE 2.0.13 ar(:,1:K-1) = ar(:,1:K-1) - ar(:,K*ones(K-1,1)) .* ar(:,K-1:-1:1); end; res(:,K+1) = res(:,K) .* (1-abs(ar(:,K)).^2); end; ACF=cumprod(ones(lr,lc)-rc.^2,2); % assign output arguments arg3=res; res=rc; MX=ar; end; %if