Why this DTFT plot from CTFT? [closed]

1. What is the difference between CTFT and DTFT?
2. Is DTFT always continuous?
3. What are the the disadvantage of DTFT?
4. What is the sufficient condition for the existence of DTFT?

What is the difference between CTFT and DTFT?

The difference is pretty quickly explained: the CTFT is for continuous-time signals, i.e., for functions x(t) with a continuous variable t∈R, whereas the DTFT is for discrete-time signals, i.e., for sequences x[n] with n∈Z.

Is DTFT always continuous?

The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the discrete Fourier transform (DFT) (see § Sampling the DTFT), which is by far the most common method of modern Fourier analysis.

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 is the sufficient condition for the existence of DTFT?

Condition for Existence of Discrete-Time Fourier Transform

The Fourier transform of a discrete-time sequence x(n) exists if and only if the sequence x(n) is absolutely summable, i.e., ∞∑n=−∞|x(n)|<∞