Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / tsa-4.2.4 / rc2ar.m

diff --git a/octave_packages/tsa-4.2.4/rc2ar.m b/octave_packages/tsa-4.2.4/rc2ar.m
new file mode 100644 (file)
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+++ b/octave_packages/tsa-4.2.4/rc2ar.m
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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.
+
+%      $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
+