1## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
2##
3## This program is free software: you can redistribute it and/or modify
4## it under the terms of the GNU General Public License as published by
5## the Free Software Foundation, either version 3 of the License, or
6## (at your option) any later version.
7##
8## This program is distributed in the hope that it will be useful,
9## but WITHOUT ANY WARRANTY; without even the implied warranty of
10## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11## GNU General Public License for more details.
12##
13## You should have received a copy of the GNU General Public License
14## along with this program; see the file COPYING. If not, see
15## <https://www.gnu.org/licenses/>.
16
17## -*- texinfo -*-
18## @deftypefn  {Function File} {} gaussian (@var{m})
19## @deftypefnx {Function File} {} gaussian (@var{m}, @var{a})
20##
21## Return a Gaussian convolution window of length @var{m}.  The width of the
22## window is inversely proportional to the parameter @var{a}.  Use larger
23## @var{a} for a narrower window.  Use larger @var{m} for longer tails.
24##
25##     w = exp ( -(a*x)^2/2 )
26##
27## for x = linspace ( -(m-1)/2, (m-1)/2, m ).
28##
29## Width a is measured in frequency units (sample rate/num samples).
30## It should be f when multiplying in the time domain, but 1/f when
31## multiplying in the frequency domain (for use in convolutions).
32## @end deftypefn
33
34function w = gaussian (m, a)
35
36  if (nargin < 1 || nargin > 2)
37    print_usage ();
38  elseif (! (isscalar (m) && (m == fix (m)) && (m > 0)))
39    error ("gaussian: M must be a positive integer");
40  elseif (nargin == 1)
41    a = 1;
42  endif
43
44  w = exp(-0.5*(([0:m-1]'-(m-1)/2)*a).^2);
45
46endfunction
47
48%!assert (gaussian (1), 1)
49
50%% Test input validation
51%!error gaussian ()
52%!error gaussian (0.5)
53%!error gaussian (-1)
54%!error gaussian (ones (1, 4))
55%!error gaussian (1, 2, 3)
56