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Two Dimensional Discrete Fourier Transform
 Syntax `dft2d(`z`)` See Also fft2 , idft2d , dft

Description
Returns the complex two-dimensional 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 -----  -----          {         __ [ (i - 1) (m - 1) / M ] } >      >      z    exp{ -2 pi \/-1 [           +         ] } -----  -----   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]} + exp{-2 pi \/-1 [(m - 1)3/4 + (n - 1)/2]} ```which is also equal to ```             __                                   __  exp{-2 pi \/-1 [(m - 1)3/4]} * ( 1 + exp{-2 pi \/-1 [(n - 1)/2]}) ```If you enter ```      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) ]      } ```
Mlmode
In Mlmode , this function is automatically included as `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) ]      } ```