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The Inverse Discrete Fourier Transform
Syntax idft(z)
See Also ifft , dft , ifft

Description
Returns a complex matrix containing the inverse discrete Fourier transform of z, where z is an integer, real double-precision or complex matrix. If N is the number of rows in z, the (k,j)-th element of the return value is equal to
         N
     1 -----                  __
     - >      z   exp[+2 pi \/-1 (i - 1) (k - 1) / N]
     N -----   i,j
       i = 1
for k between 1 and N and j between 1 and the number of columns in z.

Example
If you enter
     z = {0, 1, 0, 0}
only the term with i = 2 in the summation defining idft(z) is nonzero, and the k-th element of idft(z) is equal to
     1             __
     - exp[+2 pi \/-1 (k - 1) / 4]
     4
which is 1/4, \sqrt(-1)/4, -1/4, and -\sqrt(-1)/4, for k equal to 1, 2, 3, and 4, respectively. If you continue this example by entering
     idft(z)
O-Matrix will respond
     {
     (.25,0)
     (0,.25)
     (-.25,0)
     (0,-.25)
     }

Mlmode
In Mlmode this function is called ifft instead of idft. If you continue the example above by entering
     mlmode
     ifft(z)
O-Matrix will respond
     {
     (.25,0)
     (0,.25)
     (-.25,0)
     (0,-.25)
     }