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########################################################################
##
## Copyright (C) 1997-2024 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} =} fftshift (@var{x})
## @deftypefnx {} {@var{y} =} fftshift (@var{x}, @var{dim})
## Perform a shift of the vector @var{x}, for use with the @code{fft} and
## @code{ifft} functions, in order to move the frequency 0 to the center of
## the vector or matrix.
##
## If @var{x} is a vector of @math{N} elements corresponding to @math{N} time
## samples spaced by @nospell{@math{dt}}, then
## @code{fftshift (fft (@var{x}))} corresponds to frequencies
##
## @example
## f = [ -(ceil((N-1)/2):-1:1), 0, (1:floor((N-1)/2)) ] * df
## @end example
##
## @noindent
## where @nospell{@math{df = 1 / (N * dt)}}.
##
## If @var{x} is a matrix, the same holds for rows and columns. If @var{x}
## is an array, then the same holds along each dimension.
##
## The optional @var{dim} argument can be used to limit the dimension along
## which the permutation occurs.
## @seealso{ifftshift}
## @end deftypefn
function y = fftshift (x, dim)
if (nargin < 1)
print_usage ();
endif
if (! (isnumeric (x) || islogical (x) || ischar (x)))
error ("fftshift: X must be a vector or matrix");
endif
if (nargin == 2)
if (! (isscalar (dim) && dim > 0 && dim == fix (dim)))
error ("fftshift: dimension DIM must be a positive integer");
endif
nd = ndims (x);
sz = size (x);
sz2 = ceil (sz(dim) / 2);
idx = cell ();
idx = repmat ({':'}, nd, 1);
idx{dim} = [sz2+1:sz(dim), 1:sz2];
y = x(idx{:});
else
if (isvector (x))
xl = length (x);
xx = ceil (xl/2);
y = x([xx+1:xl, 1:xx]);
else
nd = ndims (x);
sz = size (x);
sz2 = ceil (sz ./ 2);
idx = cell ();
for i = 1:nd
idx{i} = [sz2(i)+1:sz(i), 1:sz2(i)];
endfor
y = x(idx{:});
endif
endif
endfunction
%!test
%! x = [0:7];
%! y = fftshift (x);
%! assert (y, [4 5 6 7 0 1 2 3]);
%! assert (fftshift (y), x);
%!test
%! x = [0:6];
%! y = fftshift (x);
%! assert (y, [4 5 6 0 1 2 3]);
%! assert (fftshift (y), [1 2 3 4 5 6 0]);
%!test
%! x = [0:7]';
%! y = fftshift (x);
%! assert (y, [4;5;6;7;0;1;2;3]);
%! assert (fftshift (y), x);
%!test
%! x = [0:6]';
%! y = fftshift (x);
%! assert (y, [4;5;6;0;1;2;3]);
%! assert (fftshift (y), [1;2;3;4;5;6;0]);
%!test
%! x = [0:3];
%! x = [x;2*x;3*x+1;4*x+1];
%! y = fftshift (x);
%! assert (y, [[7 10 1 4];[9 13 1 5];[2 3 0 1];[4 6 0 2]]);
%! assert (fftshift (y), x);
%!test
%! x = [0:3];
%! x = [x;2*x;3*x+1;4*x+1];
%! y = fftshift (x,1);
%! assert (y, [[1 4 7 10];[1 5 9 13];[0 1 2 3];[0 2 4 6]]);
%! assert (fftshift (y,1), x);
%!test
%! x = [0:3];
%! x = [x;2*x;3*x+1;4*x+1];
%! y = fftshift (x,2);
%! assert (y, [[2 3 0 1];[4 6 0 2];[7 10 1 4];[9 13 1 5]]);
%! assert (fftshift (y,2), x);
%!test
%! x = "abcdefg";
%! y = fftshift (x);
%! assert (y, "efgabcd");
%! assert (fftshift (y), "bcdefga");
## Test N-dimensional input
%!test <*45207>
%! x = [0:3];
%! x = x + x' + reshape (x, [1 1 4]);
%! y1 = [4 5 2 3; 5 6 3 4; 2 3 0 1; 3 4 1 2];
%! y = fftshift (x);
%! assert (y, reshape ([y1 + 2, y1 + 3, y1, y1 + 1], [4 4 4]));
%! assert (fftshift (y), x);
## Test input validation
%!error <Invalid call> fftshift ()
%!error fftshift (0:3, -1)
%!error fftshift (0:3, 0:3)
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