DTFT inconsistency

1. What are disadvantages of DTFT?
2. What is the use of DTFT?
3. Why is the DFT periodic?
4. Is the DFT of a finite length sequence periodic?

What are disadvantages of DTFT?

Two computational disadvantages of the DTFT are: the direct DTFT is a function of a continuously varying frequency and the inverse DTFT requires integration. The Fourier series coefficients constitute a periodic sequence of the same period as the signal; thus both are periodic.

What is the use of DTFT?

The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time.

Why is the DFT periodic?

The DFT is therefore said to be a frequency domain representation of the original input sequence. If the 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.

Is the DFT of a finite length sequence periodic?

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