Bispectrum on finite groups

Abstract

The algebraic theory of finite groups appears in signal processing problems involving the statistical analysis of ranked

data and the construction of invariants for pattern recognition. Standard signal processing techniques involving spectral

analysis are, in theory, possible for data defined on finite groups by using the Fourier transform provided by group representations. However, one such technique, the bispectrum, which is useful for analysing non-Gaussian data as well as

for constructing geometric invariants, has not been explored in detail for finite groups. This paper shows how to construct

the bispectrum on an arbitrary finite group or homogeneous space and explores its properties. Examples are given using

the symmetric group as well as wreath-product groups.