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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{fd} =} fractdiff (@var{x}, @var{d})
## Compute the fractional differences @math{(1-L)^d x} where @math{L}
## denotes the lag-operator and @math{d} is greater than -1.
## @end deftypefn
function retval = fractdiff (x, d)
if (nargin != 2)
print_usage ();
endif
N = 100;
if (! isvector (x))
error ("fractdiff: X must be a vector");
endif
if (! isscalar (d))
error ("fractdiff: D must be a scalar");
endif
if (d >= 1)
for k = 1 : d
x = x(2 : length (x)) - x(1 : length (x) - 1);
endfor
endif
if (d > -1)
d = rem (d, 1);
if (d != 0)
n = (0 : N)';
w = real (gamma (-d+n) ./ gamma (-d) ./ gamma (n+1));
retval = fftfilt (w, x);
retval = retval(1 : length (x));
else
retval = x;
endif
else
error ("fractdiff: D must be > -1");
endif
endfunction
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