I am new user of Mathematica, sorry if my question odd.

I not understanding, how to Mathematica apply the discrete Fourier transform for matrix:

Print[Fourier[{{-50, 50}, {50, 50}, {50, -50}}]];
(*Result is:
{{40.8248 +0. I,0. +0. I},
{-20.4124+35.3553 I,-61.2372-35.3553 I},
{-20.4124-35.3553 I,-61.2372+35.3553 I}}

Can you explain the step-by-step execution of this program using only Fourier for 1-d lists?

  • $\begingroup$ Check out Fourier in the docs. You may also want to look into a tutorial for new users - this is a good resource. $\endgroup$ – N.J.Evans Oct 18 at 12:41

Fourier does a 2D discrete Fourier transform.

You can decompose this into the individual 1D transforms using the techniques illustrated in the following example:

M = {{-50, 50}, {50, 50}, {50, -50}};
Transpose[Fourier /@ Transpose[Fourier /@ M]] == Fourier[M]
(* True *)

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