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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) ]      } ```