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fftfilt.m

## Copyright (C) 1996, 1997 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.

## -*- texinfo -*-
## @deftypefn {Function File} {} fftfilt (@var{b}, @var{x}, @var{n})
##
## With two arguments, @code{fftfilt} filters @var{x} with the FIR filter
## @var{b} using the FFT.
##
## Given the optional third argument, @var{n}, @code{fftfilt} uses the
## overlap-add method to filter @var{x} with @var{b} using an N-point FFT.
##
## If @var{x} is a matrix, filter each column of the matrix.
## @end deftypefn

## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Created: 3 September 1994
## Adapted-By: jwe
## Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
##    handle matrices

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

  transpose = rows(x) == 1;
  if transpose, x = x.'; endif
  [r_x, c_x] = size (x);
  [r_b, c_b] = size (b);
  if min ([r_b, c_b]) != 1
    error ("fftfilt: b should be a vector");
  endif
  l_b  = r_b * c_b;
  b = reshape (b, l_b, 1);

  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 (r_x + l_b - 1) / log(2)));
    B = fft (b, N);
    y = ifft(fft (x, N) .* B(:,ones(1,c_x)));
  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 (r_x / L);
    y = zeros (r_x, c_x);
    for r = 1:R;
      lo  = (r - 1) * L + 1;
      hi  = min (r * L, r_x);
      tmp = zeros(N,c_x);
      tmp(1:(hi-lo+1),:) = x(lo:hi,:);
      tmp = ifft(fft (tmp) .* B(:,ones(c_x,1)));
      hi  = min (lo+N-1, r_x);
      y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:);
    endfor
  endif

  y = y(1:r_x,:);
  if transpose, y=y.'; endif

  ## 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

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