Convert dft to dtft

1. How do you convert DTFT to DFT?
2. Is DTFT same as DFT?
3. How DFT is related to DTFT and Z transform?
4. What is the difference between DTFT and DTFS?

How do you convert DTFT to DFT?

The continuous variable found in the DTFT (ω) is replaced with a finite number of frequencies located at 2πk/NTs. Here Ts is the sampling rate. In other words, if we take the DTFT signal and sample it in the frequency domain at omega=2π/N, then we get the DFT of x(n).

Is DTFT same as DFT?

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 related to DTFT and Z transform?

Also, if r = 1, then the discrete time Fourier transform (DTFT) is same as the Z-transform. In other words, the DTFT is nothing but the Z-transform evaluated along the unit circle centred at the origin of the z-plane.

What is the difference between DTFT and DTFS?

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.