Wreath Product Cyclic Group-Based Convolution: A New Class of
Noncommutative Filters
G. Mirchandani, R. Foote, D. Rockmore, D. Healy and T. Olson
ICASSP2000
(Paper (pdf) / Paper (ps))
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. In this paper we give a brief 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.