1######################################################################## 2## 3## Copyright (C) 1997-2021 The Octave Project Developers 4## 5## See the file COPYRIGHT.md in the top-level directory of this 6## distribution or <https://octave.org/copyright/>. 7## 8## This file is part of Octave. 9## 10## Octave is free software: you can redistribute it and/or modify it 11## under the terms of the GNU General Public License as published by 12## the Free Software Foundation, either version 3 of the License, or 13## (at your option) any later version. 14## 15## Octave is distributed in the hope that it will be useful, but 16## WITHOUT ANY WARRANTY; without even the implied warranty of 17## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18## GNU General Public License for more details. 19## 20## You should have received a copy of the GNU General Public License 21## along with Octave; see the file COPYING. If not, see 22## <https://www.gnu.org/licenses/>. 23## 24######################################################################## 25 26## -*- texinfo -*- 27## @deftypefn {} {} fftshift (@var{x}) 28## @deftypefnx {} {} fftshift (@var{x}, @var{dim}) 29## Perform a shift of the vector @var{x}, for use with the @code{fft} and 30## @code{ifft} functions, in order to move the frequency 0 to the center of 31## the vector or matrix. 32## 33## If @var{x} is a vector of @math{N} elements corresponding to @math{N} time 34## samples spaced by @nospell{@math{dt}}, then 35## @code{fftshift (fft (@var{x}))} corresponds to frequencies 36## 37## @example 38## f = [ -(ceil((N-1)/2):-1:1), 0, (1:floor((N-1)/2)) ] * df 39## @end example 40## 41## @noindent 42## where @nospell{@math{df = 1 / (N * dt)}}. 43## 44## If @var{x} is a matrix, the same holds for rows and columns. If @var{x} 45## is an array, then the same holds along each dimension. 46## 47## The optional @var{dim} argument can be used to limit the dimension along 48## which the permutation occurs. 49## @seealso{ifftshift} 50## @end deftypefn 51 52function retval = fftshift (x, dim) 53 54 if (nargin != 1 && nargin != 2) 55 print_usage (); 56 endif 57 58 if (! (isnumeric (x) || islogical (x) || ischar (x))) 59 error ("fftshift: X must be a vector or matrix"); 60 endif 61 62 if (nargin == 2) 63 if (! (isscalar (dim) && dim > 0 && dim == fix (dim))) 64 error ("fftshift: dimension DIM must be a positive integer"); 65 endif 66 nd = ndims (x); 67 sz = size (x); 68 sz2 = ceil (sz(dim) / 2); 69 idx = cell (); 70 idx = repmat ({':'}, nd, 1); 71 idx{dim} = [sz2+1:sz(dim), 1:sz2]; 72 retval = x(idx{:}); 73 else 74 if (isvector (x)) 75 xl = length (x); 76 xx = ceil (xl/2); 77 retval = x([xx+1:xl, 1:xx]); 78 else 79 nd = ndims (x); 80 sz = size (x); 81 sz2 = ceil (sz ./ 2); 82 idx = cell (); 83 for i = 1:nd 84 idx{i} = [sz2(i)+1:sz(i), 1:sz2(i)]; 85 endfor 86 retval = x(idx{:}); 87 endif 88 endif 89 90endfunction 91 92 93%!test 94%! x = [0:7]; 95%! y = fftshift (x); 96%! assert (y, [4 5 6 7 0 1 2 3]); 97%! assert (fftshift (y), x); 98 99%!test 100%! x = [0:6]; 101%! y = fftshift (x); 102%! assert (y, [4 5 6 0 1 2 3]); 103%! assert (fftshift (y), [1 2 3 4 5 6 0]); 104 105%!test 106%! x = [0:7]'; 107%! y = fftshift (x); 108%! assert (y, [4;5;6;7;0;1;2;3]); 109%! assert (fftshift (y), x); 110 111%!test 112%! x = [0:6]'; 113%! y = fftshift (x); 114%! assert (y, [4;5;6;0;1;2;3]); 115%! assert (fftshift (y), [1;2;3;4;5;6;0]); 116 117%!test 118%! x = [0:3]; 119%! x = [x;2*x;3*x+1;4*x+1]; 120%! y = fftshift (x); 121%! assert (y, [[7 10 1 4];[9 13 1 5];[2 3 0 1];[4 6 0 2]]); 122%! assert (fftshift (y), x); 123 124%!test 125%! x = [0:3]; 126%! x = [x;2*x;3*x+1;4*x+1]; 127%! y = fftshift (x,1); 128%! assert (y, [[1 4 7 10];[1 5 9 13];[0 1 2 3];[0 2 4 6]]); 129%! assert (fftshift (y,1), x); 130 131%!test 132%! x = [0:3]; 133%! x = [x;2*x;3*x+1;4*x+1]; 134%! y = fftshift (x,2); 135%! assert (y, [[2 3 0 1];[4 6 0 2];[7 10 1 4];[9 13 1 5]]); 136%! assert (fftshift (y,2), x); 137 138%!test 139%! x = "abcdefg"; 140%! y = fftshift (x); 141%! assert (y, "efgabcd"); 142%! assert (fftshift (y), "bcdefga"); 143 144## Test N-dimensional input 145%!test <*45207> 146%! x = [0:3]; 147%! x = x + x' + reshape (x, [1 1 4]); 148%! y1 = [4 5 2 3; 5 6 3 4; 2 3 0 1; 3 4 1 2]; 149%! y = fftshift (x); 150%! assert (y, reshape ([y1 + 2, y1 + 3, y1, y1 + 1], [4 4 4])); 151%! assert (fftshift (y), x); 152 153## Test input validation 154%!error fftshift () 155%!error fftshift (1, 2, 3) 156%!error fftshift (0:3, -1) 157%!error fftshift (0:3, 0:3) 158