shah.m

linear time－frequency toolbox

function f=shah(L,a);
%SHAH  Discrete Shah-distribution
%  Usage: f=shah(L,a);
%
%  SHAH(L,a) computes the discrete, normalized Shah-distribution of
%  length L with a distance of a between the spikes. The Shah
%  distribution is defined by f(n*a+1)=1/sqrt(L/a) for integer n,
%  otherwise f is zero.
%
%  This is also known as a pulse train or as the comb function, because
%  the shape of the function resembles a comb. It is the sum of unit
%  impulses ('diracs') with the distance a.
%
%  The DFT of SHAH(L,a) is SHAH(L,L/a).
%
%  The Shah function has an extremely bad time-frequency localization.
%  It does not generate a Gabor frame for any L and a.
%  
%  SEE ALSO:  PGAUSS 
if nargin~=2
  error('Wrong number of input parameters.');
end;

if mod(L,a)~=0
  error('a must divide L.');
end;

f=zeros(L,1);

f(1:a:L)=1/sqrt(L/a);