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########################################################################
##
## Copyright (C) 1994-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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.
##
## 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, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{y} =} fftfilt (@var{b}, @var{x})
## @deftypefnx {} {@var{y} =} 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
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)
print_usage ();
endif
transpose = (rows (x) == 1);
if (transpose)
x = x.';
endif
[r_x, c_x] = size (x);
[r_b, c_b] = size (b);
if (! isvector (b))
error ("fftfilt: B must be a vector");
endif
if (ndims (x) != 2)
error ("fftfilt: X must be a 1-D or 2-D array");
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 ^ 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");
endif
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),:);
endfor
endif
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));
endif
## - 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));
endif
## Transpose after cleanup, otherwise rounding fails.
if (transpose)
y = y.';
endif
endfunction
%!shared b, x, r
%!testif HAVE_FFTW
%! b = [1 1];
%! x = [1, zeros(1,9)];
%! assert (fftfilt (b, x ), [1 1 0 0 0 0 0 0 0 0] );
%! assert (fftfilt (b, x.'), [1 1 0 0 0 0 0 0 0 0].');
%! assert (fftfilt (b.',x ), [1 1 0 0 0 0 0 0 0 0] );
%! assert (fftfilt (b.',x.'), [1 1 0 0 0 0 0 0 0 0].');
%! assert (fftfilt (b, [x.' x.']), [1 1 0 0 0 0 0 0 0 0].'*[1 1]);
%! assert (fftfilt (b, [x.'+2*eps x.']) == [1 1 0 0 0 0 0 0 0 0].'*[1 1],
%! [false(10, 1) true(10, 1)]);
%!testif HAVE_FFTW
%! r = sqrt (1/2) * (1+i);
%! b = b*r;
%! assert (fftfilt (b, x ), r*[1 1 0 0 0 0 0 0 0 0] , eps );
%! assert (fftfilt (b, r*x), r*r*[1 1 0 0 0 0 0 0 0 0], 2*eps);
%! assert (fftfilt (b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps );
%!testif HAVE_FFTW
%! b = [1 1];
%! x = zeros (10,3); x(1,1)=-1; x(1,2)=1;
%! y0 = zeros (10,3); y0(1:2,1)=-1; y0(1:2,2)=1;
%! y = fftfilt (b, x);
%! assert (y0, y);
%! y = fftfilt (b*i, x);
%! assert (y0*i, y);
%! y = fftfilt (b, x*i);
%! assert (y0*i, y);
%! y = fftfilt (b*i, x*i);
%! assert (-y0, y);
%! x = rand (10, 1);
%! y = fftfilt (b, [x x*i]);
%! assert (true, isreal (y(:,1)));
%! assert (false, any (real (y(:,2))));
%!testif HAVE_FFTW
%! b = rand (10, 1);
%! x = rand (10, 1);
%! y0 = filter (b, 1, x);
%! y = fftfilt (b, x);
%! assert (y0, y, 16*eps);
%! y0 = filter (b*i, 1, x*i);
%! y = fftfilt (b*i, x*i);
%! assert (y0, y, 16*eps);
%!testif HAVE_FFTW
%! b = rand (10, 1) + i*rand (10, 1);
%! x = rand (10, 1) + i*rand (10, 1);
%! y0 = filter (b, 1, x);
%! y = fftfilt (b, x);
%! assert (y0, y, 55*eps);
## Test input validation
%!error <Invalid call> fftfilt (1)
%!error fftfilt (ones (2), 1)
%!error fftfilt (2, ones (3,3,3))
%!error fftfilt (2, 1, ones (2))
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