February Fourier Talks 2014

Gerald Folland

University of Washington


Time-Frequency Analysis and the Dark Side of Representation Theory


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 so-called 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 representation-theoretic phenomena. We shall introduce the relevant concepts from representation theory, discuss the rational case briefly, and then explore the irrational case in more detail.

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