## Copyright (C) 1995-2015 Andreas Weingessel
##
## 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
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn  {Function File} {} blackman (@var{m})
## @deftypefnx {Function File} {} blackman (@var{m}, "periodic")
## @deftypefnx {Function File} {} blackman (@var{m}, "symmetric")
## Return the filter coefficients of a Blackman 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 Blackman window, see, e.g.,
## @nospell{A.V. Oppenheim & R. W. Schafer},
## @cite{Discrete-Time Signal Processing}.
## @end deftypefn

## Author: AW <Andreas.Weingessel@ci.tuwien.ac.at>
## Description: Coefficients of the Blackman window

function c = blackman (m, opt)

  if (nargin < 1 || nargin > 2)
    print_usage ();
  endif

  if (! (isscalar (m) && (m == fix (m)) && (m > 0)))
    error ("blackman: 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 ('blackman: window type must be either "periodic" or "symmetric"');
    endswitch
  endif

  if (m == 1)
    c = 1;
  else
    m -= 1;
    k = (0 : m)' / N;
    c = 0.42 - 0.5 * cos (2 * pi * k) + 0.08 * cos (4 * pi * k);
  endif

endfunction


%!assert (blackman (1), 1)
%!assert (blackman (2), zeros (2,1), 1e-6)
%!assert (blackman (15), flip (blackman (15)), 5*eps)
%!assert (blackman (16), flip (blackman (16)), 5*eps)
%!test
%! N = 9;
%! A = blackman (N);
%! assert (A(ceil (N/2)), 1, 1e-6);
%! assert ([A(1), A(length (A))], zeros (1,2), 1e-6);

%!assert (blackman (15), blackman (15, "symmetric"));
%!assert (blackman (16)(1:15), blackman (15, "periodic"));
%!test
%! N = 16;
%! A = blackman (N, "periodic");
%! assert (A(N/2 + 1), 1, 1e-6);

%!error blackman ()
%!error blackman (0.5)
%!error blackman (-1)
%!error blackman (ones (1,4))
%!error blackman (1, "invalid");