NEW DESIGN METHODS FOR TWO-DIMENSIONAL
CIRCULARLY SYMMETRIC DIGITAL FILTERS
Thesis submitted for the degree of
Doctor of Philosophy
CHAN Chun Leung
B.Sc.(Eng.), MIEEE, MIERE
Department of Electrical and Electronic Engineering
University of Hong Kong
July 1988
ABSTRACT
Two-dimensional digital filters have found increasing
applications in various areas. The present thesis
concentrates on the topic of the design of a common kind of
two-dimensional digital filters :- circularly symmetric
filters. Although there are a number of existing design
methods for this kind of filters, many of them can be
further improved to give better performance. Numerous new
efficient design methods with high performance will be
described in this thesis. The design methods aims for three
different kinds of filters : (i) zero phase non-recursive
digital filters, (ii) recursive digital filters and (iii)
linear phase recursive digital filters.
For the design of zero-phase circular symmetric
non-recursive digital filters, a method of an enhanced
McClellan transformation is introduced. It can give good
circular approximation even at large radii of frequency.
Three design methods are introduced for circularly
symmetric recursive digital filters. In order to reduce the
computational time, all these methods make use of the
ii
one-dimensional filters. The first method employs a new
spectral transformation while the other two methods use
non-linear optimization.
For the linear phase circularly symmetric digital filter
design, three new methods are introduced. In order to
reduce the computational time and achieve the convergence of
iteration easily, the numerator and the denominator of the
filter transfer function are designed separately. In the
linear phase approximation, the first method employs the
hypergeometric series. The second method utilizes the
Bessel polynomial while the third method uses non-linear
optimization.
All the newly introduced methods are easy-to-use. Most
of them can give digital filters suitable for implementation
by VLSI second-order digital filter modules. Some of them
use sum .of powers-of-two values as the filter coefficients
so that the designed filters are suitable for multiplierless
filter implementation. Besides, some of the methods have
been further extended for multidimensional ellipsoidally and
spherically symmetric digital filter designs. Finally, for
each method, several typical examples will be given to
illustrate its performance.
iii
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