Covolution of DTFT [duplicate]

1. What happens if we apply DFT twice to a signal?
2. What is convolution property of DFT?
3. What happens if you Fourier transform twice?
4. Why is the DFT mirrored?

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.

What is convolution property of DFT?

Convolution is cyclic in the time domain for the DFT and FS cases (i.e., whenever the time domain has a finite length), and acyclic for the DTFT and FT cases. ^3.6. The convolution theorem is then. (3.23) That is, convolution in the time domain corresponds to pointwise multiplication in the frequency domain.

What happens if you Fourier transform twice?

That is, if we apply the Fourier transform twice, we get a spatially reversed version of the function.

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.