Electrical and Computer Engineering ETDs

Publication Date

9-9-1974

Abstract

This dissertation presents an analytical investigation of the requirements for stability of two dimensional digital recursive filters and the development of a new procedure which can be used to synthesize low pass digital recursive filters with approximately circularly symmetric squared magnitude characteristics.

A new approach to stability analysis of two dimensional digital recursive filters is presented. A matrix recursive equation corresponding to the recursive algorithm for the two dimensional digital recursive filter is defined. This matrix recursive equation is used to formulate necessary conditions for stability of the two dimensional digital recursive filter in terms of the magnitudes of the eigenvalues of the matrices in the matrix recursive equation. These necessary conditions for the general case are shown to be necessary and sufficient conditions for stability when the spatial frequency response characteristic for the filter in question has a particular symmetry.

Sufficient conditions for stability of the two dimensional digital recursive filter are also formulated in terms of the magnitudes of the eigenvalues of the matrices in the matrix recursive equation. Thus, stability analysis of two dimensional digital recursive filters is reduced to the simple task of examining the magnitudes of the eigen­values of matrices with constant elements.

A new procedure for the synthesis of two dimensional low pass digital recursive filters with approximately circularly symmetric squared magnitude characteristics is also presented. Such filters are particularly useful for many image processing applications. Examples of image processing applications using filters designed with this procedure are given.

Document Type

Dissertation

Language

English

Degree Name

Electrical Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

Arnold Herman Koschmann

Second Committee Member

Steven Arthur Pruess

Third Committee Member

Harold Knud Knudsen

Fourth Committee Member

Joseph Thomas Cordaro Jr

Fifth Committee Member

B. R. Hunt

Comments

Sixth Commitee Member: Samuel D. Stearns

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