What Are Linear and Circular Convolution?

In signal processing, linear convolution (or simply convolution) refers to the convolution between infinitely supported sequences and filters, while circular convolution refers to the convolution between finitely supported and circularly extended sequences and filters (circular extension makes such sequences and ...

1. What is linear convolution?
2. What is meant by circular convolution?
3. What are similarities and dissimilarities between circular and linear convolutions?
4. What is the advantage of circular convolution over linear convolution?

What is linear convolution?

Linear Convolution: Linear Convolution is a means by which one may relate the output and input of an LTI system given the system's impulse response. Clearly, it is required to convolve the input signal with the impulse response of the system.

What is meant by circular convolution?

Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT).

What are similarities and dissimilarities between circular and linear convolutions?

Linear convolution may or may not result in a periodic output signal. The output of a circular convolution is always periodic, and its period is specified by the periods of one of its inputs.

What is the advantage of circular convolution over linear convolution?

This holds in continuous time, where the convolution sum is an integral, or in discrete time using vectors, where the sum is truly a sum. It also holds for functions defined from -Inf to Inf or for functions with a finite length in time.