Group character tables in discrete transform theory

摘要

It has been shown that a transform satisfying a generalized form of the convolution theorem can be described by the group character table of an appropriate finite Abelian group G. Exact correspondence between the transform properties and the underlying group properties is established and it has been demonstrated that many of the digital signal processing problems may be solved efficiently using the group theoretic approach. Sets of permutations are fully characterized such that a permutational convolution defined with respect to them can be converted into a transform product by some invertible transform.