www.gusucode.com > 时间序列分析工具箱 - tsa源码程序 > tsa/ar2rc.m
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. % 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(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