When to use the DTFT vs the DFT (and their inverses) in analysis?

1. Why we use DFT instead of DTFT?
2. How DFT is advantageous over DTFT What are its drawbacks?
3. What is the difference between DTFS and DTFT?
4. What is DTFT it is used to?

Why we use DFT instead of DTFT?

DFT (Discrete Fourier Transform) is a practical version of the DTFT, that is computed for a finite-length discrete signal. The DFT becomes equal to the DTFT as the length of the sample becomes infinite and the DTFT converges to the continuous Fourier transform in the limit of the sampling frequency going to infinity.

How DFT is advantageous over DTFT What are its drawbacks?

DTFT gives a higher number of frequency components. DFT gives a lower number of frequency components. DTFT is defined from minus infinity to plus infinity, so naturally, it contains both positive and negative values of frequencies. DFT is defined from 0 to N-1; it can have only positive frequencies.

What is the difference between DTFS and DTFT?

The DTFS is used to represent periodic discrete-time signals in the frequency domain. It's continuous-time counterpart studied previously is the Fourier Series (FS). The DTFT is used to represent non-periodic discrete-time signals in the frequency domain.

What is DTFT it is used to?

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.