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/*Description:
This function computes the N-dimensional discrete Fourier transform of A using a Fast Fourier Transform (FFT) algorithm.
The optional vector argument SIZE may be used to specify the dimensions of the array to be used.
If an element of SIZE is smaller than the corresponding dimension of A, then the dimension of A is truncated prior to performing the FFT.
Otherwise, if an element of SIZE is larger than the corresponding dimension, then A is resized and padded with zeros.
Calling sequence:
Y = fftn(A)
Y = fftn(A, SIZE)
Parameters:
A: Matrix, the input data for which the FFT is computed.
SIZE: Optional vector specifying the dimensions of the output array. If provided, the dimensions of A are adjusted accordingly.
Examples:
fftn([6 9 7 ;2 9 9 ;0 3 1],[2 2])
ans =
26. -10.
4. 4.
*/
function y = fftn(A, SIZE)
funcprot(0);
// Get the number of input arguments
rhs = argn(2);
// Check if the number of input arguments is valid
if rhs < 1 | rhs > 2 then
error("Wrong number of input arguments.");
end
// Perform action based on the number of input arguments
switch rhs
case 1 // If only A is provided
y = fft(A);
case 2 // If both A and SIZE are provided
// Check if A needs resizing
if size(A) == SIZE then
// No resizing needed
break;
elseif length(size(A)) ~= length(SIZE) then
error("Output size must have at least Ndims");
else
// Resize A using the resize_matrix function
A = resize_matrix(A, SIZE);
end
y = fft(A);
end
endfunction
/*
//test cases
i=%i;tol = 0.00001; pi = %pi ;
//test 1
Y = [41.0000 + 0*i ,-2.5000 + 2.5981*i ,-2.5000 - 2.5981*i ;2.0000 + 8.6603*i , 2.0000 + 3.4641*i , -8.5000 + 11.2583*i ;2.0000 - 8.6603*i , -8.5000 - 11.2583*i , 2.0000 - 3.4641*i]
assert_checkalmostequal(fftn([3 7 5;0 1 7;9 5 4]),Y,tol)
// test
assert_checkalmostequal(fftn([100 278;334 985]),[1697,-829;-941,473],tol)
assert_checkalmostequal(fftn([2:5;8 7 5 1;7 3 4 5;0 0 1 6],[2 2]),[20,0;-10,-2],tol)
assert_checkalmostequal(fftn([[i 2+3*i 2+pi;pi i+2 pi+i;1 5+2*5*i pi+10*i]],[2,2]),[7.1416 + 5.0000*i , -0.8584 - 3.0000*i; -3.1416 + 3.0000*i , -3.1416 - 1.0000*i],tol)
//error
fftn([2:5;8 7 5 1;7 3 4 5;0 0 1 6],[2]);
*/
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