## Date of Award

Spring 1980

## Document Type

Dissertation - Restricted

## Degree Name

Doctor of Philosophy (PhD)

## Department

Electrical and Computer Engineering

## First Advisor

Sedivy, John K.

## Second Advisor

Jaskolski, Stanley V.

## Third Advisor

Heinen, James A.

## Abstract

It is a customary procedure in analysis of physical systems to make "predictions" about particular physical situations on the basis of a theoretical model and then to compare these predictions with experimental data. Such a procedure in which available parameters of a physical model determine expected experimental results is usually called a direct problem. Inverse problems are characterized by an opposite methodology when an attempt is made to reconstruct parameters of a system directly from the experimental data. Numerous investigations have shown that inverse problems are really important applied problems, with interdisciplinary characteristics. Unfortunately for the subject, its theoretical aspects are complicated. In practice, it is only when traditional methods fail that physicists and engineers remember that studying inverse procedures is the only complete way of analyzing experimental results. A one dimensional inverse scattering problem in an important example of inverse procedure. In such a problem a "potential" function [formula] is to be determined in the Schrodinger-type operator [formula] from asymptotic properties of its solutions. Theoretical aspects of this problem have been well established and usually are known as Gelfand-Marchenko theory. Several attempts have been made in the past fifteen years to use this theory for is available. Hyperbolic systems that can be associated with a given eignevalue problem provide an important linkage between a characteristic of perturbation and properties of transformation operator. Examples of hyperbolic systems which can be associated with transmission line equations have been derived in this dissertation. Their importance and suggestions concerning the further research in this direction are also discussed.