## Copyright (C) 1995, 1996, 1997 Kurt Hornik <Kurt.Hornik@ci.tuwien.ac.at>
## Copyright (C) 2000 Paul Kienzle <pkienzle@users.sf.net>
## 
## 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/>.

## usage:  kaiser (L, beta)
##
## Returns the filter coefficients of the L-point Kaiser window with
## parameter beta.
##
## For the definition of the Kaiser window, see A. V. Oppenheim &
## R. W. Schafer, "Discrete-Time Signal Processing".
##
## The continuous version of width L centered about x=0 is:
##
##         besseli(0, beta * sqrt(1-(2*x/L).^2))
## k(x) =  -------------------------------------,  L/2 <= x <= L/2
##                besseli(0, beta)
##
## See also: kaiserord

function w = kaiser (L, beta = 0.5)

  if (nargin < 1)
    print_usage;
  elseif !(isscalar (L) && (L == round (L)) && (L > 0))
    error ("kaiser:  L has to be a positive integer");
  elseif !(isscalar (beta) && (beta == real (beta)))
    error ("kaiser:  beta has to be a real scalar");
  endif
  
  if (L == 1)
    w = 1;
  else
    m = L - 1;
    k = (0 : m)';
    k = 2 * beta / m * sqrt (k .* (m - k));
    w = besseli (0, k) / besseli (0, beta);
  endif

endfunction

%!demo
%! % use demo("kaiserord");
