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The Discrete Fourier Transform
Syntax dft(z)
See Also fft , idft , fft , lombft

Description
Returns a complex matrix containing the 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
     -----                  __
     >      z   exp[-2 pi \/-1 (i - 1) (k - 1) / 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 dft(z) is nonzero, and the k-th element of dft(z) is equal to
                 __
     exp[-2 pi \/-1 (k - 1) / 4]

which is 1, -\sqrt(-1), -1, and \sqrt(-1), for k equal to 1, 2, 3, and 4, respectively. If you continue this example by entering
     dft(z)
O-Matrix will respond
     {
     (1,0)
     (0,-1)
     (-1,0)
     (0,1)
     }

Mlmode
In Mlmode this function is called fft instead of dft. If you continue the example above by entering
     mlmode
     fft(z)
O-Matrix will respond
     {
     (1,0)
     (0,-1)
     (-1,0)
     (0,1)
     }