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25
26## -*- texinfo -*-
27## @deftypefn  {} {} fftconv (@var{x}, @var{y})
28## @deftypefnx {} {} fftconv (@var{x}, @var{y}, @var{n})
29## Convolve two vectors using the FFT for computation.
30##
31## @code{c = fftconv (@var{x}, @var{y})} returns a vector of length equal to
32## @code{length (@var{x}) + length (@var{y}) - 1}.  If @var{x} and @var{y}
33## are the coefficient vectors of two polynomials, the returned value is the
34## coefficient vector of the product polynomial.
35##
36## The computation uses the FFT by calling the function @code{fftfilt}.  If
37## the optional argument @var{n} is specified, an N-point FFT is used.
38## @seealso{deconv, conv, conv2}
39## @end deftypefn
40
41function c = fftconv (x, y, n)
42
43  if (nargin < 2 || nargin > 3)
44    print_usage ();
45  endif
46
47  if (! (isvector (x) && isvector (y)))
48    error ("fftconv: both A and B must be vectors");
49  endif
50  la = length (x);
51  lb = length (y);
52  if ((la == 1) || (lb == 1))
53    c = x * y;
54  else
55    lc = la + lb - 1;
56    x(lc) = 0;
57    y(lc) = 0;
58    if (nargin == 2)
59      c = fftfilt (x, y);
60    else
61      if (! isscalar (n))
62        error ("fftconv: N must be a scalar");
63      endif
64      c = fftfilt (x, y, n);
65    endif
66  endif
67
68endfunction
69
70
71## FIXME: Borrow tests from conv.m.  May need tolerance on the assert stmt.
72%!testif HAVE_FFTW
73%! x = ones (3,1);
74%! y = ones (1,3);
75%! b = 2;
76%! c = 3;
77%! assert (fftconv (x, x), [1; 2; 3; 2; 1], 5*eps);
78%! assert (fftconv (y, y), [1, 2, 3, 2, 1], 5*eps);
79%! assert (fftconv (x, y), [1, 2, 3, 2, 1], 5*eps);
80%! assert (fftconv (y, x), [1; 2; 3; 2; 1], 5*eps);
81%! assert (fftconv (c, x), [3; 3; 3], 5*eps);
82%! assert (fftconv (c, y), [3, 3, 3], 5*eps);
83%! assert (fftconv (x, c), [3; 3; 3], 5*eps);
84%! assert (fftconv (y, c), [3, 3, 3], 5*eps);
85%! assert (fftconv (b, c), 6, 5*eps);
86
87%!test
88%! a = 1:10;
89%! b = 1:3;
90%! assert (size (conv (a,b)), [1, numel(a)+numel(b)-1]);
91%! assert (size (conv (b,a)), [1, numel(a)+numel(b)-1]);
92
93%! a = (1:10).';
94%! b = 1:3;
95%! assert (size (conv (a,b)), [numel(a)+numel(b)-1, 1]);
96%! assert (size (conv (b,a)), [numel(a)+numel(b)-1, 1]);
97
98%!test
99%! a = 1:10;
100%! b = (1:3).';
101%! assert (size (conv (a,b)), [1, numel(a)+numel(b)-1]);
102%! assert (size (conv (b,a)), [1, numel(a)+numel(b)-1]);
103
104## Test input validation
105%!error fftconv (1)
106%!error fftconv (1,2,3,4)
107%!error fftconv ([1, 2; 3, 4], 3)
108%!error fftconv (2, [])
109%!error fftconv ([1,1], [2,2] , [3, 4])
110