Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / welchwin.m

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+## Copyright (C) 2007 Muthiah Annamalai <muthiah.annamalai@uta.edu>
+## Copyright (C) 2008-2009 Mike Gross <mike@appl-tech.com>
+## Copyright (C) 2008-2009 Peter V. Lanspeary <pvl@mecheng.adelaide.edu.au>
+##
+## 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/>.
+
+## -*- 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
+
+function [w] = welchwin(L,c)
+  if (nargin < 1 || nargin>2 )
+    print_usage;
+  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=[0:L-1];
+%! 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=[0:4*L-1];
+%! 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)