Systems Seminar
Stable Extensions of Polynomials and Architecture-Driven Filter Transformations
Prof. Nigel Boston
UW Math & ECE Departments
Abstract
A major problem in VLSI signal processing is the design of IIR filters.
Pipelining transforms the filter into one with improved throughput.
I will show that this amounts to the following mathematical problem.
Given real numbers $a_1,...,a_M$ and integer $L > M$, find the
polynomial $1 + a_1z^{-1} + ... + a_Mz^{-M} + ... + a_Lz^{-L}$ whose
pole radius (i.e. largest absolute value of a root) is smallest. Various
algorithms exist to produce polynomials with small pole radius. I will
give a new method that produces a short list of polynomials one of which
must be the pole radius minimizer. This then yields the provably best
polynomial in record time. This will be illustrated using practical
examples and we will see a considerable reduction in hardware overhead
over existing techniques. This talk will be accessible to a general audience.
Time and Place: Wed., Oct. 23, at 3:30 in 4610 Engr. Hall.
SYSTEMS SEMINAR WEB PAGE:
http://www.cae.wisc.edu/~gubner/seminar/