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 an impulse 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.
%
% If a divides L, then 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.
%
% Examples:
% ---------
%
% A simple spectrogram of the Shah function (includes the negative
% frequencies to display the whole TF-plane):
%
% sgram(shah(256,16),'dynrange',80,'nf')
%
%
% Url: http://ltfat.github.io/doc/fourier/shah.html
% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% 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/>.
% AUTHOR : Peter L. Søndergaard
% TESTING: OK
% REFERENCE: OK
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);