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.