## Copyright (C) 1996 John W. Eaton
##
## 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 2, 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, write to the Free
## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.

## usage:  fftfilt (b, x [, N])
##
## y = fftfilt (b, x) filters x with the FIR filter b using the FFT.
## y = fftfilt (b, x, N) uses the overlap-add method to filter x with
## b using an N-point FFT.
##
## Reference:  Oppenheim & Schafer (1989).  Discrete-time Signal
## Processing (Chapter 8).  Prentice-Hall.

## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Created: 3 September 1994
## Adapted-By: jwe

function y = fftfilt (b, x, N)

  ## If N is not specified explicitly, we do not use the overlap-add
  ## method at all because loops are really slow.  Otherwise, we only
  ## ensure that the number of points in the FFT is the smallest power
  ## of two larger than N and length(b).  This could result in length
  ## one blocks, but if the user knows better ...

  if (nargin < 2 || nargin > 3)
    usage (" fftfilt (b, x [, N])");
  endif

  [r_x, c_x] = size (x);
  [r_b, c_b] = size (b);
  if (! (min ([r_x, c_x]) == 1 || min ([r_b, c_b]) == 1))
    error ("fftfilt: both x and b should be vectors");
  endif
  l_x  = r_x * c_x;
  l_b  = r_b * c_b;

  if ((l_x == 1) && (l_b == 1))
    y = b * x;
    return;
  endif

  x = reshape (x, 1, l_x);
  b = reshape (b, 1, l_b);

  if (nargin == 2)
    ## Use FFT with the smallest power of 2 which is >= length (x) +
    ## length (b) - 1 as number of points ...
    N    = 2^(ceil (log (l_x + l_b - 1) / log(2)));
    y    = ifft (fft (x, N) .* fft(b, N));
  else
    ## Use overlap-add method ...
    if !(is_scalar (N))
      error ("fftfilt: N has to be a scalar");
    endif
    N = 2^(ceil (log (max ([N, l_b])) / log(2)));
    L = N - l_b + 1;
    B = fft (b, N);
    R = ceil (l_x / L);
    y = zeros (1, l_x);
    for r = 1:R;
      lo  = (r - 1) * L + 1;
      hi  = min (r * L, l_x);
      tmp = ifft (fft (x(lo:hi), N) .* B);
      hi  = min (lo+N-1, l_x);
      y(lo:hi) = y(lo:hi) + tmp(1:(hi-lo+1));
    endfor
  endif

  y = reshape (y(1:l_x), r_x, c_x);

  ## Final cleanups:  if both x and b are real respectively integer, y
  ## should also be

  if (! (any (imag (x)) || any (imag (b))))
    y = real (y);
  endif
  if (! (any (x - round (x)) || any (b - round (b))))
    y = round (y);
  endif

endfunction
