dgt.m

linear time－frequency toolbox

function [c,Ls]=dgt(f,g,a,M,L)
%DGT  Discrete Gabor transform.
%   Usage:  c=dgt(f,g,a,M);
%           c=dgt(f,g,a,M,L);
%           [c,Ls]=dgt(f,g,a,M);
%           [c,Ls]=dgt(f,g,a,M,L);
%
%   Input parameters:
%         f     : Input data
%         g     : Window function.
%         a     : Length of time shift.
%         M     : Number of modulations.
%         L     : Length of transform to do.
%   Output parameters:
%         c     : M*N array of coefficients.
%         Ls    : Length of input signal.
%
%   DGT(f,g,a,M) computes the Gabor coefficients of the input
%   signal f with respect to the window g and parameters a and M. The
%   output is a vector/matrix in a rectangular layout.
%
%   The length of the transform will be the smallest multiple of a and M that is
%   larger than the signal. f will be zero-extended to the length of the 
%   transform. If f is a matrix, the transformation is applied to each column.
%
%   The length of the transform done can be obtained by L=size(c,2)*a;   
%
%   DGT(f,g,a,M,L) computes the Gabor coefficients as above, but does
%   a transform of length L. f will be cut or zero-extended to length L before
%   the transform is done.
%
%   [c,Ls]=DGT(f,g,a,M) or [c,Ls]=DGT(f,g,a,M,L) additionally returns the
%   length of the input signal f. This is handy for reconstruction:
% 
%                [c,Ls]=dgt(f,g,a,M);
%                fr=idgt(c,gd,a,Ls);
% 
%   will reconstruct the signal f no matter what the length of f is, provided
%   that gd is a dual window of g.
%
%   The Discrete Gabor Transform is defined as follows: Consider a window g
%   and a one-dimensional signal f of length L and define N=L/a.
%   The output from c=DGT(f,g,a,M) is then given by
% 
%                  L-1 
%     c(m+1,n+1) = sum f(l+1)*exp(-2*pi*i*m*l/M)*conj(g(l-a*n+1)), 
%                  l=0  
% 
%   where m=0,...,M-1 and n=0,...,N-1.
% 
%   SEE ALSO:  IDGT, DWILT, CANTIGHT
% 
%   EXAMPLES:  EXAMP_DGT
% 
%   REFERENCES:
%     H. Feichtinger and T. Strohmer. Gabor analysis and algorithms. Theory and
%     applications. Birkhäuser, Boston, 1998.
%     
%     K. Gröchenig. Foundations of time-frequency analysis. Appl. Numer. Harmon.
%     Anal. Birkhäuser Boston, Boston, MA, 2001.

%   AUTHOR : Peter Soendergaard.

% Assert correct input.

error(nargchk(4,5,nargin));

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

assert_squarelat(a,M,1,'DGT',0);

% Change f to correct shape.
[f,Ls,W,wasrow,remembershape]=comp_sigreshape_pre(f,'DGT',0);

Lwindow=size(g,1);

if nargin<5
  [b,N,L]=assert_L(-Ls,Lwindow,a,M,'DGT');
else
  [b,N,L]=assert_L(L,Lwindow,a,M,'DGT');
end;

f=postpad(f,L);  

c=comp_dgt(f,g,a,M,L);

c=reshape(c,M,N,W);