function [x,z]=mvfilter(B,A,x,z) % Multi-variate filter function % % Y = MVFILTER(B,A,X) % [Y,Z] = MVFILTER(B,A,X,Z) % % Y = MVFILTER(B,A,X) filters the data in matrix X with the % filter described by cell arrays A and B to create the filtered % data Y. The filter is a "Direct Form II Transposed" % implementation of the standard difference equation: % % a0*Y(n) = b0*X(:,n) + b1*X(:,n-1) + ... + bq*X(:,n-q) % - a1*Y(:,n-1) - ... - ap*Y(:,n-p) % % A=[a0,a1,a2,...,ap] and B=[b0,b1,b2,...,bq] must be matrices of % size Mx((p+1)*M) and Mx((q+1)*M), respectively. % a0,a1,...,ap, b0,b1,...,bq are matrices of size MxM % a0 is usually the identity matrix I or must be invertible % X should be of size MxN, if X has size NxM a warning % is raised, and the output Y is also transposed. % % A simulated MV-AR process can be generiated with % Y = mvfilter(eye(M), [eye(M),-AR],randn(M,N)); % % A multivariate inverse filter can be realized with % [AR,RC,PE] = mvar(Y,P); % E = mvfilter([eye(M),-AR],eye(M),Y); % % see also: MVAR, FILTER % $Revision: 4585 $ % $Id: mvfilter.m 4585 2008-02-04 13:47:45Z adb014 $ % Copyright (C) 1996-2003 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, see <http://www.gnu.org/licenses/>. [ra, ca] = size(A); [rb, cb] = size(B); [M, N ] = size(x); if (ra~=rb), fprintf(2,'ERROR MVFILTER: number of rows of A and B do not fit\n'); return; end; if nargin<4, z = []; %zeros(M,oo); end; if (M~=ra), if (N==ra), fprintf(2,'Warning MVFILTER: dimensions fit only to transposed data. X has been transposed.\n'); x = x.'; %[x,z] = mvfilter(B,A,x,z); x = x.'; return; else fprintf(2,'ERROR MVFILTER: dimensions do not fit\n'); return; end; end; p = ca/M-1; q = cb/M-1; oo = max(p,q); if isempty(z) z = zeros(M,oo); else if any(size(z)~=[M,oo]) fprintf('Error MVFILTER: size of z does not fit\n'); [size(z),oo,M] return; end; end; %%%%% normalization to A{1}=I; if p<=q, for k=1:p, %A{k}=A{k}/A{1}; A(:,k*M+(1:M)) = A(:,k*M+(1:M)) / A(:,1:M); end; A(:,1:M) = eye(M); else for k=0:q, %B{k}=B{k}/A{1}; B(:,k*M+(1:M)) = B(:,k*M+(1:M)) / A(:,1:M); end; end; for k = 1:N, acc = B(:,1:M) * (x(:,k) + z(:,1)); % / A{1}; z = [z(:,2:oo), zeros(M,1)]; for l = 1:q, z(:,l) = z(:,l) + B(:,l*M+(1:M)) * x(:,k); end; for l = 1:p, z(:,l) = z(:,l) - A(:,l*M+(1:M)) * acc; end; x(:,k) = acc; end;

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