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########################################################################
##
## Copyright (C) 1995-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{c} =} hanning (@var{m})
## @deftypefnx {} {@var{c} =} hanning (@var{m}, "periodic")
## @deftypefnx {} {@var{c} =} hanning (@var{m}, "symmetric")
## Return the filter coefficients of a Hanning window of length @var{m}.
##
## If the optional argument @qcode{"periodic"} is given, the periodic form
## of the window is returned. This is equivalent to the window of length
## @var{m}+1 with the last coefficient removed. The optional argument
## @qcode{"symmetric"} is equivalent to not specifying a second argument.
##
## For a definition of the Hanning window see, e.g.,
## @nospell{A.V. Oppenheim & R. W. Schafer},
## @cite{Discrete-Time Signal Processing}.
## @end deftypefn
function c = hanning (m, opt)
if (nargin < 1)
print_usage ();
endif
if (! (isscalar (m) && m > 0 && m == fix (m)))
error ("hanning: M must be a positive integer");
endif
N = m - 1;
if (nargin == 2)
switch (opt)
case "periodic"
N = m;
case "symmetric"
## Default option, same as no option specified.
otherwise
error ('hanning: window type must be either "periodic" or "symmetric"');
endswitch
endif
if (m == 1)
c = 1;
else
m -= 1;
c = 0.5 - 0.5 * cos (2 * pi * (0 : m)' / N);
endif
endfunction
%!assert (hanning (1), 1)
%!assert (hanning (2), zeros (2,1))
%!assert (hanning (15), flip (hanning (15)), 5*eps)
%!assert (hanning (16), flip (hanning (16)), 5*eps)
%!test
%! N = 15;
%! A = hanning (N);
%! assert (A(ceil (N/2)), 1);
%!assert (hanning (15), hanning (15, "symmetric"))
%!assert (hanning (16)(1:15), hanning (15, "periodic"))
%!test
%! N = 16;
%! A = hanning (N, "periodic");
%! assert (A(N/2 + 1), 1);
%!error <Invalid call> hanning ()
%!error hanning (0.5)
%!error hanning (-1)
%!error hanning (ones (1,4))
%!error hanning (1, "invalid")
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