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## Copyright (C) 2001-2013 Paul Kienzle
##
## 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} {} interpft (@var{x}, @var{n})
## @deftypefnx {Function File} {} interpft (@var{x}, @var{n}, @var{dim})
##
## Fourier interpolation. If @var{x} is a vector, then @var{x} is
## resampled with @var{n} points. The data in @var{x} is assumed to be
## equispaced. If @var{x} is a matrix or an N-dimensional array, the
## interpolation is performed on each column of @var{x}. If @var{dim} is
## specified, then interpolate along the dimension @var{dim}.
##
## @code{interpft} assumes that the interpolated function is periodic,
## and so assumptions are made about the endpoints of the interpolation.
##
## @seealso{interp1}
## @end deftypefn
## Author: Paul Kienzle
## 2001-02-11
## * initial version
## 2002-03-17 aadler
## * added code to work on matrices as well
## 2006-05-25 dbateman
## * Make it matlab compatiable, cutting out the 2-D interpolation
function z = interpft (x, n, dim)
if (nargin < 2 || nargin > 3)
print_usage ();
endif
if (! (isscalar (n) && n == fix (n)))
error ("interpft: N must be a scalar integer");
endif
if (nargin == 2)
if (isrow (x))
dim = 2;
else
dim = 1;
endif
endif
nd = ndims (x);
if (dim < 1 || dim > nd)
error ("interpft: invalid dimension DIM");
endif
perm = [dim:nd, 1:(dim-1)];
x = permute (x, perm);
m = rows (x);
inc = ceil (m/n);
y = fft (x) / m;
k = ceil (m / 2);
sz = size (x);
sz(1) = n * inc - m;
idx = repmat ({':'}, nd, 1);
idx{1} = 1:k;
z = cat (1, y(idx{:}), zeros (sz));
idx{1} = k+1:m;
z = cat (1, z, y(idx{:}));
## When m is an even number of rows, the FFT has a single Nyquist bin.
## If zero-padded above, distribute the value of the Nyquist bin evenly
## between the new corresponding positive and negative frequency bins.
if (sz(1) > 0 && k == m/2)
idx{1} = n * inc - k + 1;
tmp = z(idx{:}) / 2;
z(idx{:}) = tmp;
idx{1} = k + 1;
z(idx{:}) = tmp;
endif
z = n * ifft (z);
if (inc != 1)
sz(1) = n;
z = inc * reshape (z(1:inc:end), sz);
endif
z = ipermute (z, perm);
endfunction
%!demo
%! clf;
%! t = 0 : 0.3 : pi; dt = t(2)-t(1);
%! n = length (t); k = 100;
%! ti = t(1) + [0 : k-1]*dt*n/k;
%! y = sin (4*t + 0.3) .* cos (3*t - 0.1);
%! yp = sin (4*ti + 0.3) .* cos (3*ti - 0.1);
%! plot (ti, yp, 'g', ti, interp1(t, y, ti, "spline"), 'b', ...
%! ti, interpft (y, k), 'c', t, y, "r+");
%! legend ("sin(4t+0.3)cos(3t-0.1)", "spline", "interpft", "data");
%!shared n,y
%! x = [0:10]'; y = sin(x); n = length (x);
%!assert (interpft (y, n), y, 20*eps);
%!assert (interpft (y', n), y', 20*eps);
%!assert (interpft ([y,y],n), [y,y], 20*eps);
%% Test case with complex input from bug #39566
%!test
%! x = (1 + j) * [1:4]';
%! y = ifft ([15 + 15*j; -6; -1.5 - 1.5*j; 0; -1.5 - 1.5*j; -6*j]);
%! assert (interpft (x, 6), y, 10*eps);
%% Test for correct spectral symmetry with even/odd lengths
%!assert (max (abs (imag (interpft ([1:8], 20)))), 0, 20*eps);
%!assert (max (abs (imag (interpft ([1:8], 21)))), 0, 21*eps);
%!assert (max (abs (imag (interpft ([1:9], 20)))), 0, 20*eps);
%!assert (max (abs (imag (interpft ([1:9], 21)))), 0, 21*eps);
%% Test input validation
%!error interpft ()
%!error interpft (1)
%!error interpft (1,2,3)
%!error <N must be a scalar integer> interpft (1,[2,2])
%!error <N must be a scalar integer> interpft (1,2.1)
%!error <invalid dimension DIM> interpft (1,2,0)
%!error <invalid dimension DIM> interpft (1,2,3)
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