Why do we need DFT when we already have DTFT/DTFS?

1. Why do you need DFT even though you have DTFT?
2. What is the advantages of DFT over DTFT?
3. Why do we need DFT in image processing?
4. What is the relationship between DTFT and DFT?

Why do you need DFT even though you have 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 advantages of DFT over DTFT?

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.

Why do we need DFT in image processing?

In image processing, the samples can be the values of pixels along a row or column of a raster image. The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers.

What is the relationship between DTFT and DFT?

The DFT differs from the discrete-time Fourier transform (DTFT) in that its input and output sequences are both finite; it is therefore said to be the Fourier analysis of finite-domain (or periodic) discrete-time functions.