|
Date: 10/12/08 + 17/12/08
Venue: MG229
Speaker: Dr. Venkatesh K Subramanian
Affiliation:Indian Institute of Technology Kanpur, India
Seminar Title: A General Theory of Signals and Processing
Part 1: The Formalism 10/12/08
Abstract
A General Theory of Signals and Processing: The Formalism Signal and System Theory is common knowledge to every electrical engineer, and its present form is the result of about two centuries of development. It is a collection of very powerful concepts encapsulated in a certain mathematical form, and this form, we hold is incidental to its historical origins and its development. While ongoing research in the numerous application areas explores the consequences of the theory and its founding postulates, the full exploitation of the power of the underlying concepts is constrained by the specific mathematical form. Our thesis seeks to generalize the concepts of signal and system theory, well beyond the familiar domains, and to formulate a mathematical framework that is highly general and primitive, yet rigorous enough to maintain the logic of the theory. We rewrite the theory in the language of Zermelo Fraenkel Set Theory (with the axioms of Choice and Regularity assumed), and express familiar notions of linearity, time/shift invariance, stability in the new framework.
Part 2: Representation Theory, Offshoots 17/12/08
Abstract
Following the first lecture, we proceed to examine the convention theory of signal representation and its intimate relationship with the processing of the signals, and seek to find a sufficiently broad definition of signal representation. The new theory of signal representation and approximation is formulated in the same set-theoretic framework already established, and the notions of secondary, tertiary, etc. signal processing systems are introduced. The theories of invariance, stability, etc are finally integrated with the representation theory, to finally present a meta-theory of transforms, that allows and directs the development of application-specific signal transforms. Conventional Fourier analysis is shown to be a special case. In the end, we present some subsequent developments in the area including rank-invariant set theory, signal processing on relations and hyper processing.
Biography
Completed B.E. from BMS engineering College in Electronics in 1987. MTech from the Electrical Engineering Department of IIT Kanpur over 1987-1989, with a dissertation in the area of Rational Choice Theory, titled "Additive Conjoint Measurement Over Incomplete Orders" that provides a theoretical framework for rational decision making under conditions of incomplete choice information. Was a PhD student at IIT Kanpur's Electrical Engineering Dept over 1989-95, working on a geometrical-topological reformulation of Signal and System Theory, titled "Signals and Systems on Sets" that sought to relax many of the mathematical assumptions made in conventional theory. Worked in IIT Guwahati from 1995 until mid 1999 as assistant professor in the Electronics and Communication Engineering Dept. Moved to IIT Kanpur's Electrical Engineering Department in 1999 and have since concerned myself with problems in the applied areas of image/video processing, computer vision with applications in video surveillance, robot navigation, visual metrology and human computer interfaces, and the mathematical modeling of drug delivery and dissemination in the context of hormone based approaches to male contraception.
|
