Given a signal $\mathbf{z} \in \mathbb{C}^n$ and its Discrete Fourier transform $\hat{\mathbf{z} }$, does $||\mathbf{z}|| = ||\hat{\mathbf{z} }||$ hold?

The question is given to me like this with no additional details. Information about what kind of norm is also not given. Does anyone have an idea what the question might be looking for?


I may consider them as L^2 then following theorem holds.




Also keen to learn if there is any other theorems.

  • $\begingroup$ So the relation does not hold, correct? $\endgroup$
    – Karla
    Feb 2 '20 at 11:40
  • $\begingroup$ It holds but L^2 norm. $\endgroup$
    – jomegaA
    Feb 2 '20 at 11:41

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