D'Alotto L.A., Giardina C.R., Luo H. A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing

Издательство Marcel Dekker, 1998, -300 pp.A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing is a text dedicated to a modern approach in signal processing. A timely concern in the digital signal processing area is parallel processing. While numerous works have appeared on parallel computer architectures, relatively little information has been documented on the underlying principle for creating parallel digital signal processing algorithms to be used in these computers. This book fills the void by providing a unified signal algebra approach for creating parallel digital signal processing algorithms.
Parallel representations of basic signal processing operations occur naturally in the algebraic setting set forth herein. In the unified signal algebra approach, all operations are defined on digital signals, not on individual numbers that constitute the signals. Indeed, the arguments of all signal processing operations are functions represented by matrices – NOT NUMBERS. A matrix type representation, called a bound matrix, is used in describing digital signals. This representation, in the time domain, provides a useful alternative to the Z-transform representation of digital signals. It captures all essential features of digital signals and provides necessary compression.
Operations on digital signals are specified using block diagrams. Together with bound matrices, the block diagram presentation provides a universal language for the description of important parallel digital signal processing algorithms. Throughout, an abundance of examples and execution type traces of block diagram algorithms are given. Many exercises are also presented. The exercises are intended to serve as an aid to understanding the material.
In terms of six fundamental operations, all other digital signal processing operations are formed under function composition. This is consistent with reduced instruction set computer philosophy, whereby a "small number of building blocks" can be used to form useful operations. Each of the six fundamental operations is induced by similar operations in the domain or range space and it is this technique that provides the unified algebraic methodology. While the methodology contained herein is useful in various signal processing environments, this text is self-contained and always remains at a "how to" level.
Two dimensional digital signal processing is mainly concerned with the extraction of information from signals. The steps involved in the information extraction procedure include some or all of the following: digital signal creation, digital signal to digital signal operation, digital signal to real number operation, real number to decision operation
In this book, we concentrate on step 2 above. Essentially, the primary and only difference between two dimensional and single dimensional signal processing is greater computational complexity when dealing with the higher dimensional signals.
Even though various digital signal processing techniques are independent of dimension, the representation of such signals is dimensionally dependent. Matrix type notation, called bound matrices, is used to represent two dimensional digital signals. This structure is introduced in the first chapter and employed throughout.
All parallel algorithms are specified using block diagrams. This allows easily describable traces and walk-throughs of all algorithms and is consistent with data flow procedural descriptions.
Using two dimensional signals allows for a rich processing environment. This environment is exploited by using two dimensional techniques for efficient processing of single dimensional digital signals. Indeed, the last chapter of the text is dedicated to this type of optimization.
Two dimensional wraparound signal processing is also presented in the text. A self-contained chapter describes the algebraic environment necessary for processing these types of signals. Again, bound matrix representation is introduced and block diagram specification of all algorithms is given.
This book is intended to be used as a text in digital signal processing courses for graduate students. It also provides a useful reference for applied mathematicians, computer scientists, and electrical engineers who are interested in algebraic techniques for providing parallel algorithms.Two Dimensional Signals
Fundamental Operations on Two Dimensional Signals
Convolution of Digital Signals
Z Transforms
Difference Equations
Wraparound Signal Processing
Parallel Multidimensional Algorithms for Single Dimensional Signal Processing
A: Set Operations and Morphology for Two Dimensional Digital Signal Processing