Time scaling of discrete-time sequences and the DTFT

1. What is the key difference between the DFT and DTFT?
2. What is the relation between DTFT and DFT?
3. What are the differences between discrete-time Fourier transform DTFT and discrete Fourier transform DFT )? Explain DFT in detail with the help of examples and diagrams?
4. What is the difference between DTFS and DTFT?

What is the key difference between the DFT and DTFT?

original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic Page 2 function, the DFT provides all the non-zero values of one DTFT cycle.

What is the relation between DTFT and 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.

What are the differences between discrete-time Fourier transform DTFT and discrete Fourier transform DFT )? Explain DFT in detail with the help of examples and diagrams?

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.