12-04-2017, 02:26 PM
Linear convolution takes two functions of an independent variable, which I will call time, and convolves them using the convolution sum formula that you could find in a book of signal processing or digital signals. Basically it is a correlation of one function with the inverted version in time of the other function. I think of it as flipping, multiplying and adding as one function changes from the other. This is fulfilled in continuous time, where the sum of convolution is integral, or in discrete time using vectors, where the sum is really a sum. It also applies to functions defined from -Inf to Inf or functions with a finite length in time.
Circular convolution is only defined for functions of finite length (usually, perhaps always, equal in length), continuous or discrete in time. In circular convolution, it is as if finite-length functions are periodically repeated over time. Because the input functions are now periodic, the convoluted output is also periodic and therefore the convoluted output is fully specified by one of its periods.
It can be understood in the following video:
