Speaker:      Jean-Charles Faugere and Fabrice Rouillier
Title:        Design of filter and filter banks using dedicated Computer
              Algebra Tools
Affiliation:  Equipe Calcul Formel (LIP6)  
              Chercheur CNRS 
              and
              Loria / Inria-Lorraine 
URL:          http://posso.lip6.fr/~jcf/ and http://www.loria.fr/~rouillie/ 
EMail:        Jean-Charles.Faugere@lip6.fr and Fabrice.Rouillier@loria.fr

Abstract

In theory it is well known that Computer Algebra techniques and more especially
polynomial systems solving methods can be used to design filter or filter
banks.  On the other hand general computer algebra systems are not powerful
enough to handle such problems.

Fortunately, recent progress in algorithms for solving polynomial systems have
enhanced the computational capabilities of dedicated computer algebra systems.
On the basis of the prospective work done in the European Frisco project we
consider in this talk five problems in Signal Theory that lead to algebraic
systems.  We describe new algorithms and software that have been used for
solving these problems. In particular we mention very efficient algorithms for
computing exactly all the real roots of a zero dimensional system.  A
surprising fact is that very often the algebraic systems are not zero
dimensional so that we need special algorithms and software to ``solve'' such
systems: decomposition of the variety, special routine to draw curve of high
degree, testing emptiness of hyper surfaces.