# ParaHerm

H = ParaHerm(G)

## SYNOPSIS function H = ParaHerm(G);

## DESCRIPTION ```H = ParaHerm(G)

Returns the parahermitian (i.e. the complex conjugate transpose, time
reversed matrix) of the MIMO system matrix G.

If G represents a polynomial matrix G(z) of order L with
G(z) = G0 + G1 z^{-1} + G2 z^{-2} + ... + GL z^{-L}
then
G(:,:,1) = G0;
G(:,:,2) = G1;
G(:,:,3) = G2;
...
G(:,:,L) = GL;
The parahermitian H(z) = G~(z) is given by
H(:,:,1)   = GL';
...
H(:,:,L-1) = G1';
H(:,:,L)   = G0';
Note that (.)' is the Hermitian transpose operator.

Input parameter:
H      K x N x L    MIMO system matrix

Output parameter:
G      N x K x L    MIMO system matrix```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:

## SOURCE CODE ```0001 function H = ParaHerm(G);
0002 %H = ParaHerm(G)
0003 %
0004 %   Returns the parahermitian (i.e. the complex conjugate transpose, time
0005 %   reversed matrix) of the MIMO system matrix G.
0006 %
0007 %   If G represents a polynomial matrix G(z) of order L with
0008 %      G(z) = G0 + G1 z^{-1} + G2 z^{-2} + ... + GL z^{-L}
0009 %   then
0010 %      G(:,:,1) = G0;
0011 %      G(:,:,2) = G1;
0012 %      G(:,:,3) = G2;
0013 %      ...
0014 %      G(:,:,L) = GL;
0015 %   The parahermitian H(z) = G~(z) is given by
0016 %      H(:,:,1)   = GL';
0017 %      ...
0018 %      H(:,:,L-1) = G1';
0019 %      H(:,:,L)   = G0';
0020 %   Note that (.)' is the Hermitian transpose operator.
0021 %
0022 %   Input parameter:
0023 %      H      K x N x L    MIMO system matrix
0024 %
0025 %   Output parameter:
0026 %      G      N x K x L    MIMO system matrix
0027
0028 % S Weiss, Univ of Southampton, 15/7/2004
0029
0030 [M,N,L] = size(G);
0031 H = zeros(N,M,L);
0032 for m = 1:M,
0033   for n = 1:N,
0034      H(n,m,:) = conj(G(m,n,end:-1:1));
0035   end;
0036 end;
0037```

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