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welchwin.m

## Copyright (C) 2007   Muthiah Annamalai  <muthiah.annamalai@uta.edu>
## Copyright (C) 2008   Mike Gross, Peter V. Lanspeary
##
## 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 2 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/>.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{w}] =} welchwin(@var{L},@var{c})
## Returns a row vector containing a Welch window, given by 
## @var{w}(n)=1-(n/N-1)^2,   n=[0,1, ... @var{L}-1].
## Argument @var{L} is the length of the window.
## Optional argument @var{c} specifies a "symmetric" window (the default),
## or a "periodic" window.
##
## A symmetric window has zero at each end and maximum in the middle;
## @var{L} must be an integer larger than 2.
## @code{if c=="symmetric", N=(L-1)/2}
##
## A periodic window wraps around the cyclic interval [0,1, ... @var{L}-1],
## and is intended for use with the DFT  (functions fft(),
## periodogram() etc).
## @var{L} must be an integer larger than 1.
## @code{if c=="periodic", N=@var{L}/2}.
##
## @seealso{blackman, kaiser}
## @end deftypefn

## changelog
##  2007-  Muthiah Annamalai, <muthiah.annamalai@uta.edu>
##       original code
##  2009-01-02  Mike Gross, <mike@appl-tech.com>
##       symmetric window
##  2009-01-06  Peter Lanspeary, <pvl@mecheng.adelaide.edu.au>
##       add 2nd arg and demo; update documentation string and arg checking

function  = welchwin(L,c)
  if (nargin < 1 || nargin>2 )
    usage('welchwin(L,[c])');
  endif
  symmetric=1;
  if ( nargin==2 && ! isempty(c) )
    if ( ! ischar(c) || size(c,1) != 1 ||
         ( ! strcmp(c,'periodic') && ! strcmp(c,'symmetric') ) )
      error( "arg 2 (c) must be \"periodic\" or \"symmetric\"" )
    endif
    symmetric = ! strcmp(c,'periodic');
  endif
  ##
  ## Periodic window is not properly defined if L<2.
  ## Symmetric window is not properly defined if L<3.
  min_L = 2 + symmetric;
  if ( ! isreal(L) || ! isscalar(L) || L<min_L || fix(L) != L )
    error("arg 1 (L) must be an integer larger than %d", min_L-1 );
  endif
  N = (L-symmetric)/2;
  n = 0:L-1;
  w = 1 - ((n-N)./N).^2;
endfunction;

%!demo
%! printf( "Short symmetric windows\n" );
%! welchwin(5)
%! welchwin(6)
%! welchwin(6,"symmetric")
%! welchwin(7)
%! input( "Press ENTER to continue", "s" );
%!
%! printf( "Short periodic windows\n" );
%! welchwin(6,"periodic")
%! welchwin(7,"periodic")
%! input( "Press ENTER to continue", "s" );
%!
%! L=32;
%! printf( "Graph: single period of " );
%! printf( "%d-point periodic (blue) and symmetric (red) windows\n", L );
%! t=;
%! xp=welchwin(L,"periodic");
%! xs=welchwin(L,"symmetric");
%! plot(t,xp,"b",t,xs,"r")
%! input( "Press ENTER to continue", "s" );
%!
%! printf( "Graph: 4 periods of " );
%! printf( "%d-point periodic (blue) and symmetric (red) windows\n", L );
%! t2=;
%! xp2=repmat(xp,1,4);
%! xs2=repmat(xs,1,4);
%! plot(t2,xp2,"b",t2,xs2,"r")
%! input( "Press ENTER to continue", "s" );
%!
%! n=512;
%! s=fftshift(max(1.0e-2,abs(fft(postpad(xp,n)))));
%! f=[-0.5:1/n:0.5-1/n];
%! printf( "%dx null-padded, power spectrum of %d-point window\n", n/L, L );
%! semilogy(f,s)


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