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## Copyright (C) 1995, 1996, 1997 Friedrich Leisch
##
## This program 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 2, or (at your option)
## any later version.
##
## This program 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 this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: fractdiff(x, d)
##
## Computes the fractional differences (1-L)^d x where L denotes the
## lag-operator and d > -1.
## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Description: Compute fractional differences
function retval = fractdiff (x, d)
N = 100;
if !is_vector (x)
error ("fractdiff: x must be a vector")
endif
if !is_scalar (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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