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Two Dimensional Inverse Discrete Fourier Transform
Syntax idft2d(z)
See Also ifft2 , dft2d , idft

Description
Returns the complex two-dimensional inverse discrete Fourier transform of z, where z is an integer, real, double-precision or complex matrix. If 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
 1   -----  -----          {         __ [ (i - 1) (m - 1) / M ] }
---  >      >      z    exp{ +2 pi \/-1 [           +         ] }
N M  -----  -----   i,j    {            [ (j - 1) (n - 1) / N ] }
     i = 1  j = 1

If the only prime factors of 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.

Example
In the following example 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]}/8 + exp{+2 pi \/-1 [(m - 1)3/4 + (n - 1)/2]}/8

which is also equal to
            __                                   __ 
exp{+2 pi \/-1 [(m - 1)3/4]} * ( 1 + exp{+2 pi \/-1 [(n - 1)/2]}) / 8

If you enter
     z = [{0, 0, 0, 1}, {0, 0, 0, 1}]
     idft2d(z)
O-Matrix replies
     {
     [ (0.25,0) , (0,0) ]
     [ (0,-0.25) , (0,0) ]
     [ (-0.25,0) , (0,0) ]
     [ (0,0.25) , (0,0) ]
     }

Mlmode
In Mlmode , this function is automatically included as ifft2 instead of idft2d. If in Mlmode you enter
     z = [0 0 0 1; 0 0 0 1]';
     ifft2(z)
O-Matrix replies
     {
     [ (.25,0)  , (0,0) ]
     [ (0,-.25) , (0,0) ]
     [ (-.25,0) , (0,0) ]
     [ (0,.25)  , (0,0) ]
     }