external/octave/oc_fftfilt.m
% Copyright (C) 1994-2015 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 3 of the License, or (at
% your option) any later version.
%
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% 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
% <http://www.gnu.org/licenses/>.

% -*- texinfo -*-
% @deftypefn  {Function File} {} fftfilt (@var{b}, @var{x})
% @deftypefnx {Function File} {} fftfilt (@var{b}, @var{x}, @var{n})
% Filter @var{x} with the FIR filter @var{b} using the FFT.
%
% If @var{x} is a matrix, filter each column of the matrix.
%
% 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@.
% The FFT size must be an even power of 2 and must be greater than or equal to
% the length of @var{b}.  If the specified @var{n} does not meet these
% criteria, it is automatically adjusted to the nearest value that does.
%
% @seealso{filter, filter2}
% @end deftypefn

% Author: Kurt Hornik <Kurt.Hornik@wu-wien.ac.at>
% Created: 3 September 1994
% Adapted-By: jwe

function y = oc_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)
    print_usage ();
  end

  transpose = (size(x,1) == 1);

  if (transpose)
    x = x.';
  end

  [r_x, c_x] = size (x);
  [r_b, c_b] = size (b);

  if (~isvector (b))
    error ('fftfilt: B must be a vector');
  end

  if (ndims (x) ~= 2)
    error ('fftfilt: X must be a 1-D or 2-D array');
  end

  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 ^ nextpow2 (r_x + l_b - 1);
    B = fft (b, n);
    y = ifft (fft (x, n) .* B(:, ones (1, c_x)));
  else
    % Use overlap-add method ...
    if (~(isscalar (n)))
      error ('fftfilt: N has to be a scalar');
    end
    n = 2 ^ nextpow2 (max ([n, l_b]));
    L = n - l_b + 1;
    B = fft (b, n);
    B = B(:, ones (c_x,1));
    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);
      hi  = min (lo+n-1, r_x);
      y(lo:hi,:) = y(lo:hi,:) + tmp(1:(hi-lo+1),:);
    end
  end

  y = y(1:r_x, :);

  % Final cleanups:

  % - If both b and x are real, y should be real.
  % - If b is real and x is imaginary, y should be imaginary.
  % - If b is imaginary and x is real, y should be imaginary.
  % - If both b and x are imaginary, y should be real.
  xisreal = all (imag (x) == 0);
  xisimag = all (real (x) == 0);

  if (all (imag (b) == 0))
    y (:,xisreal) = real (y (:,xisreal));
    y (:,xisimag) = complex (real (y (:,xisimag)) * 0, imag (y (:,xisimag)));
  elseif (all (real (b) == 0))
    y (:,xisreal) = complex (real (y (:,xisreal)) * 0, imag (y (:,xisreal)));
    y (:,xisimag) = real (y (:,xisimag));
  end

  % - If both x and b are integer in both real and imaginary
  %   components, y should be integer.
  if (~any(b - fix (b)))
    idx = find (~any(x - fix (x)));
    y (:, idx) = round (y (:, idx));
  end

  % Transpose after cleanup, otherwise rounding fails.
  if (transpose)
    y = y.';
  end

end
