Circular convolution of two length- sequences uses modular arithmetic for their indices. Extending both inputs periodically gives the displayed formula. Equivalently, fold a finite discrete convolution into residue classes modulo by adding entries whose indices are congruent. The discrete Fourier transform of the circular convolution is the product of the two discrete Fourier transforms, with the usual unnormalized forward transform and inverse convention.
Circular convolution is a mathematical operation used primarily in signal processing and systems analysis, specifically when dealing with finite-length signals and systems. It is a variant of convolution that takes into account the periodic nature of signals when the signals are considered to be circularly wrapped around.
New to topics? Read the docs here!