DFT algorithm output meanning [duplicate]

1. What does output of DFT mean?
2. Why is the DFT mirrored?
3. What happens if we apply DFT twice to a signal?
4. Is output of DFT periodic?

What does output of DFT mean?

DFT output (m), in simpe terms, is the correlation of the input sequence with the complex exponential sequence of period m.

Why is the DFT mirrored?

Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way.

What happens if we apply DFT twice to a signal?

Applying the DFT twice results in a scaled, time reversed version of the original series. The transform of a constant function is a DC value only.

Is output of DFT periodic?

the DFT spectrum is periodic with period N (which is expected, since the DTFT spectrum is periodic as well, but with period 2π).