--- /dev/null
+function [MX,res,arg3] = ar2rc(ar);
+% converts autoregressive parameters into reflection coefficients
+% with the Durbin-Levinson recursion for multiple channels
+% function [AR,RC,PE] = ar2rc(AR);
+% function [MX,PE] = ar2rc(AR);
+%
+% INPUT:
+% AR autoregressive model parameter
+%
+% 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)
+% AR = 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 RC2AR
+%
+% 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: ar2rc.m 5090 2008-06-05 08:12:04Z schloegl $
+% Copyright (C) 1998-2002,2008 by Alois Schloegl <a.schloegl@ieee.org>
+%
+% 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(ar);
+res=[ones(lr,1) zeros(lr,lc)];
+
+if nargout<3 % needs O(p^2) memory
+ MX=zeros(lr,lc*(lc+1)/2);
+ MX(:,lc*(lc-1)/2+(1:lc))=ar;
+
+ % Durbin-Levinson Algorithm
+ idx=lc*(lc-1)/2;
+ for K=lc:-1:2;
+ %idx=K*(K-1)/2; %see below
+ MX(:,(K-2)*(K-1)/2+(1:K-1)) = (MX(:,idx+(1:K-1)) + MX(:,(idx+K)*ones(K-1,1)).*MX(:,idx+(K-1:-1:1)))./((ones(lr,1)-abs(MX(:,idx+K)).^2)*ones(1,K-1));
+ idx=idx-K+1;
+ end;
+ for K=1:lc
+ idx=K*(K-1)/2; %see below
+ res(:,K+1) = res(:,K).*(1-abs(MX(:,idx+K)).^2);
+ end;
+
+ %arp=MX(:,K*(K-1)/2+(1:K));
+ %rc =MX(:,(1:K).*(2:K+1)/2);
+
+else % needs O(p) memory
+
+ %ar=zeros(lr,lc);
+ rc=zeros(lr,lc);
+ rc(:,lc)=ar(:,lc);
+ MX=ar; % assign output
+
+ % Durbin-Levinson Algorithm
+ for K=lc-1:-1:1,
+ ar(:,1:K)=(ar(:,1:K)+ar(:,(K+1)*ones(K,1)).*ar(:,K:-1:1))./((ones(lr,1)-abs(ar(:,K+1)).^2)*ones(1,K));
+ rc(:,K)=ar(:,K);
+ end;
+
+ for K=1:lc,
+ res(:,K+1) = res(:,K) .* (1-abs(ar(:,K)).^2);
+ end;
+
+ % assign output arguments
+ arg3=res;
+ res=rc;
+ %MX=ar;
+end; %if