--- /dev/null
+
+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
+
+% $Id: mvfilter.m 6981 2010-03-02 23:38:34Z schloegl $
+% Copyright (C) 1996-2003 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/>.
+
+
+[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;
+