--- /dev/null
+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.
+
+% $Id: rc2ar.m 5090 2008-06-05 08:12:04Z schloegl $
+% Copyright (c) 1996-2002,2007,2008 by Alois Schloegl <a.schloegl@ieee.org>
+% This function is part of the TSA-toolbox
+% http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/tsa/
+%
+% 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/>.
+
+
+% 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
+