Wreath product cyclic group-based convolution: a new class of noncommutative filters

The theory of spectral analysis of a particular class of noncommutative groups-wreath products of cyclic groups-has been shown to have a group-based convolution that leads to a new class of noncommutative filters. These filters, with their group and scale-selective properties and their relationship to DFT filter banks, offer some intriguing possibilities in signal processing applications. We give a summary of some of the basic properties of convolution with wreath product cyclic groups and illustrate those properties through an example. Applications to some basic signal processing tasks are proposed