Why do we need circular convolution?

1. Why do we learn circular convolution?
2. Why do we use circular convolution in DFT?
3. Where do we use circular convolution?
4. What is the importance of linear and circular convolution?

Why do we learn circular convolution?

Although DTFTs are usually continuous functions of frequency, the concepts of periodic and circular convolution are also directly applicable to discrete sequences of data. In that context, circular convolution plays an important role in maximizing the efficiency of a certain kind of common filtering operation.

Why do we use circular convolution in DFT?

The convolution is circular because of the periodic nature of the DFT sequence. Recall that an N-point DFT of an aperiodic sequence is periodic with a period of N. Also recall that the IDFT is essentially a DFT with a small difference.

Where do we use circular convolution?

"Circular convolution is used to convolve two discrete Fourier transform (DFT) sequences." MATLAB documentation says this. To me, circular convolution is an operation on any sequences.

What is the importance of linear and circular convolution?

Linear convolution is the basic operation to calculate the output for any linear time invariant system given its input and its impulse response. Circular convolution is the same thing but considering that the support of the signal is periodic (as in a circle, hence the name).