update packages

[CreaPhase.git] / octave_packages / m / signal / fftfilt.m

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+## Copyright (C) 1994-2012 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.
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- 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.
+## @seealso{filter, filter2}
+## @end deftypefn
+
+## Author: Kurt Hornik <Kurt.Hornik@wu-wien.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)
+    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, :);
+  if (transpose)
+    y = y.';
+  endif
+
+  ## Final cleanups: If both x and b are real, y should be real.
+  ## If both x and b are integer, y should be integer.
+
+  if (isreal (b) && isreal (x))
+    y = real (y);
+  endif
+  if (! any (b - fix (b)))
+    idx = !any (x - fix (x));
+    y(:, idx) = round (y(:, idx));
+  endif
+
+endfunction
+
+
+%!shared b, x, r
+%!test
+%!  b = [1 1];
+%!  x = [1, zeros(1,9)];
+%!  assert(fftfilt(b,  x  ), [1 1 0 0 0 0 0 0 0 0]  , eps);
+%!  assert(fftfilt(b,  x.'), [1 1 0 0 0 0 0 0 0 0].', eps);
+%!  assert(fftfilt(b.',x  ), [1 1 0 0 0 0 0 0 0 0]  , eps);
+%!  assert(fftfilt(b.',x.'), [1 1 0 0 0 0 0 0 0 0].', eps);
+
+%!test
+%!  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], eps);
+%!  assert(fftfilt(b, x.'), r*[1 1 0 0 0 0 0 0 0 0].', eps);
+
+%!test
+%!  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 (y,y0);
+
+%!test
+%!  b  = rand (10, 1);
+%!  x  = rand (10, 1);
+%!  y0 = filter (b, 1, x);
+%!  y  = filter (b, 1, x);
+%!  assert (y, y0);
+
+%% Test input validation
+%!error fftfilt (1)
+%!error fftfilt (1, 2, 3, 4)
+%!error fftfilt (ones (2), 1)
+%!error fftfilt (2, ones (3,3,3))
+%!error fftfilt (2, 1, ones (2))
+