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function g=firkaiser(L,beta,varargin)
%-*- texinfo -*-
%@deftypefn {Function} firkaiser
%@verbatim
%FIRKAISER Kaiser-Bessel window
% Usage: g=firkaiser(L,beta);
% g=firkaiser(L,beta,...);
%
% FIRKAISER(L,beta) computes the Kaiser-Bessel window of length L with
% parameter beta. The smallest element of the window is set to zero when
% the window has an even length. This gives the window perfect whole-point
% even symmetry, and makes it possible to use the window for a Wilson
% basis.
%
% FIRKAISER takes the following flags at the end of the input arguments:
%
% 'normal' Normal Kaiser-Bessel window. This is the default.
%
% 'derived' Derived Kaiser-Bessel window.
%
% 'wp' Generate a whole point even window. This is the default.
%
% 'hp' Generate half point even window.
%
% Additionally, FIRKAISER accepts flags to normalize the output. Please
% see the help of NORMALIZE. Default is to use 'peak' normalization.
%
%
% References:
% A. V. Oppenheim and R. W. Schafer. Discrete-time signal processing.
% Prentice Hall, Englewood Cliffs, NJ, 1989.
%
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/sigproc/firkaiser.html}
%@seealso{firwin, normalize}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% 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/>.
if nargin<2
error('Too few input arguments.');
end;
if numel(beta)>1
error('beta must be a scalar.');
end;
% Define initial value for flags and key/value pairs.
definput.import={'normalize'};
definput.importdefaults={'null'};
definput.flags.centering={'wp','hp'};
definput.flags.stype={'normal','derived'};
[flags,keyvals]=ltfatarghelper({},definput,varargin);
cent=0;
if flags.do_hp
cent=.5;
end;
if flags.do_normal
if (L == 1)
g = 1;
else
m = L - 1;
k = (0:L-1)'+rem(L,2)/2-.5+cent;
k = 2*beta/(L-1)*sqrt(k.*(L-1-k));
g = besseli(0,k)/besseli(0,beta);
end;
g=ifftshift(g);
if ((flags.do_wp && rem(L,2)==0) || ...
(flags.do_hp && rem(L,2)==1))
% Explicitly zero last element. This is done to get the right
% symmetry, and because that element sometimes turn negative.
g(floor(L/2)+1)=0;
end;
else
if rem(L,2)==1
error('The length of the choosen window must be even.');
end;
if flags.do_wp
if rem(L,4)==0
L2=L/2+2;
else
L2=L/2+1;
end;
else
L2=floor((L+1)/2);
end;
% Compute a normal Kaiser window
g_normal=fftshift(firkaiser(L2,beta,flags.centering));
g1=sqrt(cumsum(g_normal(1:L2))./sum(g_normal(1:L2)));
if flags.do_wp
if rem(L,2)==0
g=[flipud(g1);...
g1(2:L/2)];
else
g=[flipud(g1);...
g1(1:floor(L/2))];
end;
else
g=[flipud(g1);...
g1];
end;
if ((flags.do_wp && rem(L,2)==0) || ...
(flags.do_hp && rem(L,2)==1))
% Explicitly zero last element. This is done to get the right
% symmetry, and because that element sometimes turn negative.
g(floor(L/2)+1)=0;
end;
end;
% The besseli computation sometimes generates a zero imaginary component.
g=real(g);
g=normalize(g,flags.norm);
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