comp_dwilt.m

linear time－frequency toolbox

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

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;