The convolution theorem shows us that there are two ways to perform circular convolution.
Remember ... this still gives us cyclic convolution
Idea: If we add enough trailing zeros to the signals being convolved, we can get the same results as in acyclic convolution (in which the convolution summation goes from to ).
Question: How many zeros do we need to add?
A sampling-theorem based insight:
Zero-padding in the time domain results in more samples (closer spacing) in the frequency domain. This can be thought of as a higher `sampling rate' in the frequency domain. If we have a high enough frequency-domain sampling rate, we can avoid time domain aliasing.