Speaker:      Markus Pueschel
Title:        Group Representations and Automatic Derivation of Fast Signal
              Transforms
Affiliation:  Mathematics and Computer Science
              Drexel University and Carnegie Mellon University
              Philadelphia, PA USA
URL:          http://avalon.ira.uka.de/home/pueschel/
Email:        pueschel@ece.cmu.edu

Abstract

Using methods from group representation theory it is possible to derive
automatically many fast signal transforms including the FFT and fast
trigonometric transforms.  The approach we use consists of two steps.  First
the symmetry of the transform is determined.  Second a decomposition of the
transform is derived from the symmetry using constructive representation
theory.  This procedure has been implemented in the GAP share package AREP and
successfully applied to a large number of signal transforms.

This shows a strong relationship between discrete signal transforms and
representation theory, opening a new area of research to exploit the benefits
of this connection.