idgt.m

linear time－frequency toolbox

function [f]=idgt(coef,g,a,Ls)
%IDGT  Inverse discrete Gabor transform.
%   Usage:  f=idgt(c,g,a);
%           f=idgt(c,g,a,Ls);
%
%   Input parameters:
%         c     : Array of coefficients.
%         g     : Window function.
%         a     : Length of time shift.
%         Ls    : length of signal.
%   Output parameters:
%         f     : Signal.
%
%   IDGT(c,g,a) computes the Gabor expansion of the input coefficients
%   c with respect to the window g and time shift a. The number of 
%   channels is deduced from the size of the coefficients c.
%
%   IDGT(c,g,a,Ls) does as above but cuts or extends f to length Ls.
%
%   For perfect reconstruction, the window used must be a dual window of the
%   one used to generate the coefficients.
%
%   Assume that f=IDGT(c,g,a,L) for an array c of size M x N. 
%   Then the following holds for k=0,...,L-1: 
% 
%             N-1 M-1          
%   f(l+1)  = sum sum c(m+1,n+1)*exp(2*pi*i*m*l/M)*g(l-a*n+1)
%             n=0 m=0          
%  
%   SEE ALSO:  DGT, DWILT, CANTIGHT

% AUTHOR : Peter Soendergaard.

% Check input paramameters.

error(nargchk(3,4,nargin));

if prod(size(g))==1
  error('g must be a vector (you probably forgot to supply the window function as input parameter.)');
end;

wasrow=0;

if size(g,2)>1
  if size(g,1)>1
    error('g must be a vector');
  else
    % g was a row vector.
    g=g(:);

    % If the input window is a row vector, the output signal will also
    % be a row vector.
    wasrow=1;
  end;
end;

Lwindow=size(g,1);


M=size(coef,1);
N=size(coef,2);
W=size(coef,3);

% use assert_squarelat to check a and the window size.
assert_squarelat(a,M,1,'IDGT');
[b,Njunk,Lout]=assert_L(0,Lwindow,a,M,'IDGT');

L=N*a;

if Lout>L
  error('Window is too long.');
end;

% Do the actual computation.
f=comp_idgt(coef,g,a,M,L);

% Cut or extend f to the correct length, if desired.
if nargin==4
  f=postpad(f,Ls);
else
  Ls=L;
end;

f=comp_sigreshape_post(f,Ls,wasrow,[0; W]);