pgauss.m

linear time－frequency toolbox

function [g]=pgauss(L,tfr,cent)
%PGAUSS  Sampled, periodized Gaussian.
%   Usage: g=pgauss(L);
%          g=pgauss(L,tfr);
%          g=pgauss(L,tfr,cent);
% 
%   Input parameters:
%        L : Length of vector.
%      tfr : ratio between time and frequency support.
%     cent : Centering.
%   Output parameters:
%        g : The periodized Gaussian(s).
%
%   PGAUSS(L,tfr) computes samples of a periodized Gaussian.
%   The function returns a regular sampling of the periodization
%   of the function exp(-pi*(x.^2)).
%
%   The returned function has norm == 1.
%
%   The parameter tfr determines the ratio between the effective
%   support of g and the effective support of the DFT of g. If tfr>1 then
%   g has a wider support than the DFT of g.
%
%   PGAUSS(L) does the same setting tfr=1.
%
%   The function is whole-point even. This implies that fft(pgauss(L,tfr))
%   is real for any L and tfr.
%
%   PGAUSS(L,tft,cent) will generate a differently centered Gaussian.
%   Setting cent=0 generates a whole point centered function (as above)
%   and setting cent=.5 generates a half point centered function, as most
%   other Matlab filter routines.
%
%   If this function is used to generate a window for a Gabor frame,
%   then the optimal window is generated by PGAUSS(L,a*M/L);
%
%   SEE ALSO:  WPSPLINE, WPHANNING
%
%   EXAMPLES:  EXAMP_PGAUSS
%
%   REFERENCES:
%     S. G. Mallat and Z. Zhang. Matching pursuits with time-frequency
%     dictionaries. IEEE Trans. Signal Process., 41(12):3397-3415, 1993.

% Author : Peter Soendergaard.

%   First reference on this found in mazh93 eq. 63

error(nargchk(1,3,nargin));

if nargin==1
  tfr=1;
end;

if nargin<=2
  cent=[0, 0];
end;

if (prod(size(L,1))~=1 || ~isnumeric(L))
  error('L must be a scalar');
end;

if rem(L,1)~=0
  error('L must be an integer.')
end;

if (prod(size(tfr,1))~=1 || ~isnumeric(tfr))
  error('tfr must be a scalar.');
end;

if (prod(size(cent,1))~=1 || ~isnumeric(cent))
  error('cent must be a scalar.');
end;

g=comp_pgauss(L,tfr,cent);