Dtft

$2\pi$ periodicity of discrete-time Fourier transform

$2\pi$ periodicity of discrete-time Fourier transform
  1. Why is DTFT 2 pi periodic?
  2. What is the period of discrete Fourier transform?
  3. Does DFT assume periodicity?
  4. Is DTFS periodic?

Why is DTFT 2 pi periodic?

The discrete-time Fourier transform (DTFT) gives us a way of representing frequency content of discrete-time signals. where T is a sufficiently small sampling step. Then X(Ω) can be thought of as a discretization of X(ω). Due to discrete-time nature of the original signal, the DTFT is 2π-periodic.

What is the period of discrete Fourier transform?

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

Does DFT assume periodicity?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur).

Is DTFS periodic?

It's periodic! Figure 7.2. 9, Figure 7.2.

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