Why circular convolution is called as periodic convolution?

Circular convolution is referred to as periodic convolution because it assumes that the input sequences are periodic, effectively wrapping around at the boundaries. This means that when the sequences are convolved, the calculations treat the end of the sequences as connected to the beginning, leading to a continuous, repeating pattern. As a result, the output of circular convolution is periodic with the same period as the input sequences, contrasting with linear convolution, which extends indefinitely. This periodic nature is particularly useful in applications like digital signal processing, where such assumptions can simplify computations.