Computing the FFT of a single channel is well understood in the literature. However, computing the FFT of multiple channels in a systematic manner has not been fully addressed. This paper presents a framework to design a family of multi-channel FFT architectures using {\em folding} and {\em interleaving}. Three distinct multi-channel FFT architectures are presented in this paper. These architectures differ in the input and output preprocessing steps and are based on different folding sets, i.e., different orders of execution.