Real discrete Fourier transform

1. What is real DFT?
2. What is the difference between DTFS and DTFT?
3. Is DFT and DTFS same?
4. Why is DTFT used?

What is real DFT?

The real discrete Fourier transform (RDFT) corresponds to the Fourier series for sampled periodic signals with sampled periodic frequency responses just as discrete Fourier transform (DFT) corresponds to the complex Fourier series for the same type of signals.

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.

Is DFT and DTFS same?

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.

Why is DTFT used?

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.