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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} =} bartlett (@var{m})
## Return the filter coefficients of a Bartlett (triangular) window of length
## @var{m}.
##
## For a definition of the Bartlett window see, e.g.,
## @nospell{A.V. Oppenheim & R. W. Schafer},
## @cite{Discrete-Time Signal Processing}.
## @end deftypefn
function c = bartlett (m)
if (nargin != 1)
print_usage ();
endif
if (! (isscalar (m) && m > 0 && m == fix (m)))
error ("bartlett: M must be a positive integer");
endif
if (m == 1)
c = 1;
else
m -= 1;
n = fix (m / 2);
c = [2*(0:n)/m, 2-2*(n+1:m)/m]';
endif
endfunction
%!assert (bartlett (1), 1)
%!assert (bartlett (2), zeros (2,1))
%!assert (bartlett (15), flip (bartlett (15)), 5*eps)
%!assert (bartlett (16), flip (bartlett (16)), 5*eps)
%!test
%! N = 9;
%! A = bartlett (N);
%! assert (A(ceil (N/2)), 1);
%!error <Invalid call> bartlett ()
%!error bartlett (0.5)
%!error bartlett (-1)
%!error bartlett (ones (1,4))
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