Question

Advantages of circular convolution over linear convolution

Answer 1

Linear convolution takes two functions of an independent variable, which I will call time, and convolves them using the convolution sum formula you might find in a linear sytems or digital signal processing book. Basically it is a correlation of one function with the time-reversed version of the other function. I think of it as flip, multiply, and sum while shifting one function with respect to the other. 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. 

Answer 2

Advantages of circular convolution over linear convolution:

• Convolution is operation among functions. We usually meet it in Signal Processing where a system (LTI System) can be designated by its Impulse Response. Then its output is agreed using the linear convolution of the input and the output.

• Convolution theorem which states the correspondence between Linear Convolution in the Time Domain vs. Element Wise multiplication in the Fourier Domain.

• In the actual world, signals are discrete and finite. Therefore linear convolution isn’t feasible.

Hope it helped.....