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## -*- 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