comp_dwilt.m

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function [coef]=comp_dwilt(coef2,a)
%COMP_DWILT  Compute Discrete Wilson transform.
%   

% 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/>.

M=size(coef2,1)/2;
N=size(coef2,2);
W=size(coef2,3);
L=N*a;

coef=zeros(2*M,N/2,W);

% Unmodulated case.
coef(1,:,:)=coef2(1,1:2:N,:);

% odd value of m
coef(2:2:M,:,:)=1/sqrt(2)*i*(coef2(2:2:M,1:2:N,:)-coef2(2*M:-2:M+2,1:2:N,:));
coef(M+2:2:2*M,:,:)=1/sqrt(2)*(coef2(2:2:M,2:2:N,:)+coef2(2*M:-2:M+2,2:2:N,:));

% even value of m
coef(3:2:M,:,:)=1/sqrt(2)*(coef2(3:2:M,1:2:N,:)+coef2(2*M-1:-2:M+2,1:2:N,:));
coef(M+3:2:2*M,:,:)=1/sqrt(2)*i*(coef2(3:2:M,2:2:N,:)-coef2(2*M-1:-2:M+2,2:2:N,:));

% Nyquest case
if mod(M,2)==0
  coef(M+1,:,:) = coef2(M+1,1:2:N,:);
else
  coef(M+1,:,:) = coef2(M+1,2:2:N,:);
end;


coef=reshape(coef,M*N,W);


if 0

  % This code will work only if the input is known to come from a real valued
  % signal.

  % XXX This never happens, because the input coefficients are always
  % complex, and it is a difficult task to derive whether they are WPE in
  % frequency

  % If the input coefficients are real, the calculations can be
  % be simplified. The complex case code also works for the real case.

  % cosine, first column.
  coef(3:2:M,:,:)=sqrt(2)*real(coef2(3:2:M,1:2:N,:));
  
  % sine, second column
  coef(M+3:2:2*M,:,:)=-sqrt(2)*imag(coef2(3:2:M,2:2:N,:));
  
  % sine, first column.
  coef(2:2:M,:,:)=-sqrt(2)*imag(coef2(2:2:M,1:2:N,:));
  
  % cosine, second column
  coef(M+2:2:2*M,:,:)=sqrt(2)*real(coef2(2:2:M,2:2:N,:));

end;