Proof that DFT does not require more than N points

1. What happens if we apply DFT twice to a signal?
2. What is n-point in DFT?
3. How do you find N-point DFT?
4. Why do we need DFT although we have DTFT?

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 n-point in DFT?

Definition. An N-point DFT is expressed as the multiplication , where is the original input signal, is the N-by-N square DFT matrix, and. is the DFT of the signal.

How do you find N-point DFT?

DFT[x1(n) N x2(n)] = X1(k)X2(k) Where N indicates N-point circular convolution. Where N Indicates N-point circular convolution.

Why do we need DFT although we have DTFT?

original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic Page 2 function, the DFT provides all the non-zero values of one DTFT cycle.