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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)      } ```