Date of Award


Publication Type

Doctoral Thesis

Degree Name



Electrical and Computer Engineering


Engineering, Electronics and Electrical.




Digital processing of two dimensional signals is becoming increasingly important, and is finding applications in diverse scientific disciplines. Of the two classes of 2-D digital filters, namely recursive and nonrecursive, the first class is probably the most efficient in terms of hardware costs. However, it suffers from the stability problem as well as phase linearity, which is inherent in nonrecursive filters. This thesis will review past work on the stability problem and methods for stabilizing filters. It has been shown that only a 2-D analog transfer function with a 2-variable Very Strictly Hurwitz Polynomial--VSHP--in its denominator can produce a 2-D stable recursive digital filter upon the application of double bilinear transformation. This thesis examines the existing methods of generating a 2-variable VSHP and presents a new one. Existing design techniques for 2-D filters are briefly outlined, and a number of new methods suggested. These methods are generally iterative in nature and use linear and/or non-linear optimization techniques to determine the coefficients of the filter transfer function by minimizing an objective function which is a measure of difference between the magnitude and/or phase response of the designed and desired 2-D filter respectively. These design methods are for the general class of 2-D filters as well as a special class; separable denominator, non-separable numerator transfer function with or without circular cutoff boundaries. The design procedures presented for the special class of 2-D filters, enjoy low computation and implementation costs. This was made possible by a considerable reduction of the number of coefficients in the transfer function and the choice of two step optimization approach. This thesis also presents various strategies for the design of 2-D filters with non circular cutoff boundary, using a cascade of several 2-D filter building blocks. These building blocks are formed by a transformation of 1-D filters. This approach is very simple and yields a good approximation to the desired response. It requires a 1-D realization structure. Several modifications to these techniques are also presented to improve the accuracy of the design. A review of various realization structures for 2-D filters is presented in this thesis along with a new realization technique for a class of 2-D filters. Also, a variety of design examples are presented to illustrate the effectiveness of the proposed design techniques.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1991 .M295. Source: Dissertation Abstracts International, Volume: 53-09, Section: B, page: 4858. Thesis (Ph.D.)--University of Windsor (Canada), 1991.