Title:TimeFrequency Analysis and the Dark Side of Representation Theory
Abstract:The group of operators on generated by a single translation and a single modulation is a familiar object of study in signal analysis. It forms a unitary representation of the socalled discrete Heisenberg group. As such, its analysis yields easily to classical methods when is rational. But when is irrational, it provides instructive concrete examples of several pathological representationtheoretic phenomena. We shall introduce the relevant concepts from representation theory, discuss the rational case briefly, and then explore the irrational case in more detail.
