

Matrix Computations and Scientific Computing Seminar Department of Mathematics University of California Berkeley, CA
Efficient Matrix Computations in Adaptive Filtering with Orthonormal Basis
Functions
October 16, 2002
Adaptive filtering is a topic of immense practical value with applications
in
a wide range of areas in signal processing and communications. This talk
focuses on the class of leastsquares adaptive filters and examines two
typical implementations: one is based on a tappeddelay line realization
while the other employs orthonormal basis functions such as a Laguerre
network.
While extensive prior works in the literature have shown that fast
leastsquares
schemes are possible for tappeddelayline (Toeplitz) structures, little is
said about
efficient implementations for orthonormal networks. In this talk, we show
that
efficient orthonormal networks are possible. We do so by exploiting more
general forms of matrix structure that arise in the context of fast
leastsquares
solutions for orthonormal networks, in both cases of fixedorder
and orderrecursive algorithms. In particular, we develop a theory that
accomodates such general filter structures, and we use
it to devise exact fast leastsquares algorithms. We also comment on some
algorithmic issues that are relevant for the development of reliable
filters,
especially in quantized environments. Simulation results are used to
illustrate some
illconditioning difficulties as well as the performance of the proposed
filters.




