Design and realization of two-dimensional recursive digital filters.

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

Two dimensional recursive digital filters for near real time image processing

A program was designed toward the demonstration of the feasibility of using two dimensional recursive digital filters for subjective image processing applications that require rapid turn around. The concept of the use of a dedicated minicomputer for the processor for this application was demonstrated. The minicomputer used was the HP1000 series E with a RTE 2 disc operating system and 32K words of memory. A Grinnel 256 x 512 x 8 bit display system was used to display the images. Sample images were provided by NASA Goddard on a 800 BPI, 9 track tape. Four 512 x 512 images representing 4 spectral regions of the same scene were provided. These images were filtered with enhancement filters developed during this effort

Design of multidimensional digital filters by spectral transformations

Imperial Users onl

A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

Two-dimensional block processors - structures and implementations

Includes bibliographical references.Two-dimensional (2-D) block processing technique for linear filtering of digital images is introduced. New 2-D block structures are derived for 2-D recursive digital filters realized by difference equations and state-space formulations. Several special cases have also been considered and the relevant 2-D block structures are given. The computational costs of different implementation techniques employing high-speed convolution algorithms such as fast Fourier transform, number theoretic transform and polynomial transform have been studied. A comparison among the relative efficiencies of these implementation schemes is made and a suitable method is then proposed using short convolution algorithm which results in a minimized computational time

On analog networks and mixed-domain spatio-temporal frequency response

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