Plenary Lecture
The Convolution and Impulse Response Scandals
Professor Irwin W. Sandberg
Department of Electrical and Computer Engineering
The University of Texas at Austin
1 University Station C0803
Austin, Texas 78712 - 0240
USA
Abstract:
It is a widely-held belief that the main textbook conclusions concerning continuous-time
linear systems obtained using Dirac delta-function arguments can be shown to be
valid using the mathematical theory of distributions. But this belief is unwarranted.
For example, in a recent study of multidimensional input-output maps representing
linear shift-invariant systems that take a set of continuous-space signals into itself,
it was shown that the family contains maps – even causal continuous maps – whose
impulse response is the zero function, but which take certain inputs into nonzero outputs.
In this connection, we give recent results concerning the representation of the
input-output map associated with the members of a certain important large family
of multidimensional linear systems. We also give necessary and sufficient conditions
under which the representation can be written as a convolution, and we relate this to
the concepts of an impulse response and a q-response limit, and to the flawed concept
of the Dirac function.
Brief Biography of the Speaker:
Irwin W. Sandberg received the B.E.E., M.E.E., and D.E.E. degrees from the
Polytechnic Institute of Brooklyn (now the Polytechnic University) in 1955,
1956, and 1958, respectively (Westinghouse Fellow 1956, Bell Laboratories Fellow
1957 and 1958). He is presently an emeritus Professor of Electrical and Computer
Engineering at the University of Texas at Austin, where he holds the Cockrell
Family Regents Chair Emeritus in Engineering, No. 1. From 1958 to 1986, he was
with Bell Laboratories, Murray Hill, New Jersey, as a Member of Technical Staff
in the Communication Sciences Research Division, and, from 1967 to 1972, as Head
of the Systems Theory Research Department.
He has been concerned with the analysis of radar systems for military defense,
with synthesis and analysis of linear networks, with several studies of
qualitative properties of nonlinear systems (with emphasis on the theory of
nonlinear networks as well as on the introduction and development of
input-output stability theory), and with some problems in communication theory
and numerical analysis. His more recent interests include studies of the
approximation and signal-processing capabilities of dynamic nonlinear networks.
Dr. Sandberg received the first Technical Achievement Award of the IEEE Circuits
and Systems Society. He is a Fellow of the American Association for the
Advancement of Science, a Life Fellow of the IEEE, an IEEE Centennial Medalist,
an IEEE Millennial Medalist, a Circuits and Systems Society Golden Jubilee Medal
recipient, a former Circuits and Systems Society Distinguished Lecturer, an
Outstanding Alumnus of Polytechnic University, a former Vice Chairman of the
IEEE Group on Circuit Theory, a former Guest Editor of the IEEE TRANSACTIONS ON
CIRCUIT THEORY Special Issue on Active and Digital Networks, and a former Guest
Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS Darlington Memorial
Issue. He has published extensively and has been an advisor to American Men and
Women of Science.
He is listed in Who’s Who in America, and holds nine patents. He has received
outstanding paper awards, an ISI Press Classic Paper Citation, and a Bell
Laboratories Distinguished Staff Award. He is a member of Eta Kappa Nu, Sigma
Xi, Tau Beta Pi, the Academy of Medicine, Engineering and Science of Texas, and
the National Academy of Engineering.