psech.m

Matlab时频分析工具箱,希望能对大家有所帮助啊

function [g,tfr]=psech(L,tfr)
%PSECH  Sampled, periodized hyperbolic secant.
%   Usage: g=psech(L);
%          g=psech(L,tfr);
% 
%   Input parameters:
%        L : Length of vector.
%      tfr : ratio between time and frequency support.
%   Output parameters:
%        g : The periodized Gaussian(s).
%
%   PSECH(L,tfr) computes samples of a periodized hyperbolic secant.
%   The function returns a regular sampling of the periodization
%   of the function sech(pi*x)
%
%   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.
%
%   PSECH(L) does the same setting tfr=1.
%
%   The function is whole-point even.  This implies that FFT(PSECH(L,tfr))
%   is real for any L and tfr.
%
%   If this function is used to generate a window for a Gabor frame, then
%   the window giving the smalles frame bound ratio is generated by
%   PSECH(L,a*M/L);
% 
%   SEE ALSO:  PGAUSS, PBSPLINE, PHERM
% 
%   REFERENCES:
%     A. J. E. M. Janssen and T. Strohmer. Hyperbolic secants yield Gabor
%     frames. Appl.Comput.Harmon.Anal., 12(2):259-267, 2002.
%     

% 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/>.

error(nargchk(1,2,nargin));

if nargin==1
  tfr=1;
end;

if size(L,1)>1 || size(L,2)>1
  error('L must be a scalar');
end;

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

% Parse tfr and order.
if sum(1-(size(tfr)==1))>1
  error('tfr must be a scalar or vector');
end;

safe=12;

g=zeros(L,1);
sqrtl=sqrt(L);

w=tfr;

% Outside the interval [-safe,safe] then sech(pi*x) is numerically zero.
nk=ceil(safe/sqrt(L/sqrt(w)));

lr=(0:L-1).';
for k=-nk:nk  
  g=g+sech(pi*(lr/sqrtl-k*sqrtl)/sqrt(w));
end;

% Normalize it.
g=g*sqrt(pi/(2*sqrt(L*w)));