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dft2d(z) |
| See Also | fft2 , idft2d , dft |
M is the number of rows in
z and N is the number of columns in
z, the (m,n)-th
element of the return value is equal to
M N
----- ----- { __ [ (i - 1) (m - 1) / M ] }
> > z exp{ -2 pi \/-1 [ + ] }
----- ----- i,j { [ (j - 1) (n - 1) / N ] }
i = 1 j = 1
M and N are
2, 3, 5, and 7, the transform is done in order
(M)(N)[log(N) + log(M)] operations;
otherwise the transform is done in order
(M)(N)(N + M) operations.
M is 4, N is 2,
and the (4,1)-th and (4,2)-th elements of z
are one (the rest of the elements of z are zero).
The (m,n)-th element of the transform is therefore equal to
__ __
exp{-2 pi \/-1 [(m - 1)3/4]} + exp{-2 pi \/-1 [(m - 1)3/4 + (n - 1)/2]}
__ __
exp{-2 pi \/-1 [(m - 1)3/4]} * ( 1 + exp{-2 pi \/-1 [(n - 1)/2]})
z = [{0, 0, 0, 1}, {0, 0, 0, 1}]
dft2d(z)
O-Matrix replies
{
[ (2,0) , (0,0) ]
[ (0,2) , (0,0) ]
[ (-2,0) , (0,0) ]
[ (0,-2) , (0,0) ]
}
fft2 instead of dft2d.
If in Mlmode you enter
z = [0 0 0 1; 0 0 0 1]';
fft2(z)
O-Matrix replies
{
[ (2,0) , (0,0) ]
[ (0,2) , (0,0) ]
[ (-2,0) , (0,0) ]
[ (0,-2) , (0,0) ]
}