Why integrate over $2\pi$ in inverse DTFT?

1. Why is DTFT 2pi periodic?
2. What is inverse DTFT?
3. What are the the disadvantage of DTFT?
4. What are the necessary and sufficient condition for the existence of DTFT?

Why is DTFT 2pi periodic?

Due to discrete-time nature of the original signal, the DTFT is 2π-periodic.

What is inverse DTFT?

The inverse DTFT is the original sampled data sequence. The inverse DFT is a periodic summation of the original sequence. The fast Fourier transform (FFT) is an algorithm for computing one cycle of the DFT, and its inverse produces one cycle of the inverse DFT.

What are the the disadvantage 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 are the necessary and sufficient condition for the existence of DTFT?

Sufficient Condition for Existence of the DTFT

A sequence x[n] satisfying (7.7) is said to be absolutely summable, and when (7.7) holds, the infinite sum defining the DTFT X(ej ˆω) in (7.2) is said to converge to a finite result for all ˆω.