Dudgeon D.E. Multidimensional Digital Signal Processing

Prentice Hall, 1995. — 406 p.One of the by-products of the computer revolution has been the emergence of completely new fields of study. Each year, as integrated circuits have become faster, cheaper, and more compact, it has become possible to find feasible solutions to problems of ever-increasing complexity. Because it demands massive amounts of digital storage and comparable quantities of numerical computation, multidimensional digital signal processing is a problem area which has only recently begun to emerge. Despite this fact, it has already provided the solutions to important problems ranging from computer-aided tomography (CAT), a technique for combining x-ray projections from different orientations to create a three-dimensional recon- reconstruction of a portion of the human body, to the design of passive sonar arrays and the monitoring of the earth's resources by satellite. In addition to its many glamorous and humble applications, however, multidimensional digital signal processing also possesses a firm mathematical foundation, which allows us not only to understand what has already been accomplished, but also to explore rationally new problem areas and solution methods as they arise.
Simply stated, a signal is any medium for conveying information, and signal processing is concerned with the extraction of that information. Thus ensembles of time-varying voltages, the density of silver grains on a photographic emulsion, or lists of numbers in the memory of a computer all represent examples of signals. A typical signal processing task involves the transfer of information from one signal to another. A photograph, for example, might be scanned, sampled, and stored in the memory of a computer. In this case, the information is transferred from a variable silver density, to a beam of visible light, to an electrical waveform, and finally to a sequence of numbers, which, in turn, are represented by an arrangement of magnetic domains on a computer disk. The CAT scanner is a more complex example; information about the structure of an unknown object is first transferred to a series of electromagnetic waves, which are then sampled to produce an array of numbers, which, in turn, are processed by a computational algorithm and finally displayed on the phosphor of a cathode ray tube (CRT) screen or on photographic film. The digital processing which is done cannot add to the information, but it can rearrange it so that a human observer can more readily interpret it; instead of looking at multiple shadows the observer is able to look at a cross-sectional view.
Whatever their form, signals are of interest only because of the information they contain. At the risk of overgeneralizing we might say that signal processing is concerned with two basic tasks —information rearrangement and information reduction. We have already seen two examples of information rearrangement — computer-aided tomography and image scanning. To those we could easily add other examples: image enhancement, image deblurring, spectral analysis, and so on. Information reduction is concerned with the removal of extraneous information. Someone observing radar returns is generally interested in only a few bits of information, specifically, the answer to such questions as: Is anything there? If so, what? Friend or foe? How fast is it going, and where is it headed? However, the receiver is also giving the observer information about the weather, chaff, birds, nearby build- buildings, noise in the receiver, and so on. The observer must separate the relevant from the irrelevant, and signal processing can help. Other examples of information-lossy signal processing operations include noise removal, parameter estimation, and feature extraction.
Multidimensional Signals and Systems
Two-Dimensional Discrete signals
Multidimensional systems
Frequency-Domain Characterization of signals and systems
Sampling Continuous 2-D signals
Processing Continuous signals with Discrete Systems
Discrete Fourier Analysis of Multidimensional Signals
Discrete Fourier Series Representation of Rectangularly Periodic Sequences
Multidimensional Discrete Fourier Transform
Calculation of the Discrete Fourier Transform
Discrete Fourier Transforms for General Periodically Sampled Signals
Interrelationship between M-dimensional and One-Dimensional DFTs
Design and Implementation of Two-dimensional FIR Filters
FIR Filters
Implementation of FIR Filters
Optimal FIR Filter Design
Design of FIR Filters for Special Implementations
FIR Filters for Hexagpnally Sampled Signals
Multidimensional Recursive Systems
Finite-Order Difference Equations
Multidimensional z-Transforms
Stability of Recursive Systems
Two-Dimensional Complex Cepstrum
Design and Implementation of Two-dimensional IIR Filters
Classical 2-D IIR Filter Implementations
Iterative Implementations for 2-D IIR Filters
Signal Flowgraphs and State-Variable Realizations
Space-Domain Design Techniques
Frequency-Domain Design Techniques
Design Techniques for Specialized Structures
Stabilization Techniques
Processing Signals Carried by Propagating Waves
Beamforming
Discrete-Time Beamforming
Further Considerations for Array Processing Applications
Multidimensional Spectral Estimation
Inverse Problems
Constrained Iterative Signal Restoration
Seismic Wave Migration
Reconstruction of Signals from Their Projections
Projection of Discrete Signals