/usr/share/octave/packages/signal-1.3.2/welchwin.m is in octave-signal 1.3.2-1+b1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 | ## 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} {} welchwin (@var{m})
## @deftypefnx {Function File} {} welchwin (@var{m}, "periodic")
## @deftypefnx {Function File} {} welchwin (@var{m}, "symmetric")
## Return the filter coefficients of a Welch window of length @var{m}. The
## Welch window is given by
## @var{w}(n)=1-(n/N-1)^2, n=[0,1, ... @var{m}-1].
## The optional argument specifies a "symmetric" window (the default) or a
## "periodic" window.
##
## A symmetric window has zero at each end and maximum in the middle, and the
## length must be an integer greater than 2. The variable @var{N} in the
## formula above is @code{(@var{m}-1)/2}.
##
## A periodic window wraps around the cyclic interval [0,1, ... @var{m}-1],
## and is intended for use with the DFT. The length must be an integer
## greater than 1. The variable @var{N} in the formula above is
## @code{@var{m}/2}.
##
## @seealso{blackman, kaiser}
## @end deftypefn
function w = welchwin (m, opt)
if (nargin < 1 || nargin > 2)
print_usage ();
elseif (! (isscalar (m) && (m == fix (m)) && (m > 0)))
error ("welchwin: M must be a positive integer");
endif
N = (m - 1) / 2;
mmin = 3;
if (nargin == 2)
switch (opt)
case "periodic"
N = m / 2;
mmin = 2;
case "symmetric"
N = (m - 1) / 2;
otherwise
error ("welchwin: window type must be either \"periodic\" or \"symmetric\"");
endswitch
endif
## Periodic window is not properly defined for m < 2.
## Symmetric window is not properly defined for m < 3.
if (m < mmin)
error ("welchwin: M must be an integer greater than %d", mmin);
endif
n = [0:m-1]';
w = 1 - ((n-N)./N).^2;
endfunction
%!demo
%! m = 32;
%! t = [0:m-1];
%! printf ("Graph: single period of ");
%! printf ("%d-point periodic (blue) and symmetric (red) windows\n", m);
%! xp = welchwin (m, "periodic");
%! xs = welchwin (m, "symmetric");
%! plot (t, xp, "b", t, xs, "r")
%!demo
%! m = 32;
%! t = [0:4*m-1];
%! printf ("Graph: 4 periods of ");
%! printf ("%d-point periodic (blue) and symmetric (red) windows\n", m);
%! xp = welchwin (m, "periodic");
%! xs = welchwin (m, "symmetric");
%! xp2 = repmat (xp, 4, 1);
%! xs2 = repmat (xs, 4, 1);
%! plot (t, xp2, "b", t, xs2, "r")
%!demo
%! m = 32;
%! n = 512;
%! xp = welchwin (m, "periodic");
%! s = fftshift (max (1e-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/m, m);
%! semilogy (f, s)
%!assert (welchwin (3), [0; 1; 0]);
%!assert (welchwin (15), flipud (welchwin (15)));
%!assert (welchwin (16), flipud (welchwin (16)));
%!assert (welchwin (15), welchwin (15, "symmetric"));
%!assert (welchwin (16)(1:15), welchwin (15, "periodic"));
%% Test input validation
%!error welchwin ()
%!error welchwin (0.5)
%!error welchwin (-1)
%!error welchwin (ones (1, 4))
%!error welchwin (1, 2, 3)
%!error welchwin (1, "invalid")
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