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The theory of linear discrete time filtering started with a paper
by Kol mogorov in 1941. He addressed the problem for stationary
random se quences and introduced the idea of the innovations
process, which is a useful tool for the more general problems
considered here. The reader may object and note that Gauss
discovered least squares much earlier; however, I want to
distinguish between the problem of parameter estimation, the Gauss
problem, and that of Kolmogorov estimation of a process. This sep
aration is of more than academic interest as the least squares
problem leads to the normal equations, which are numerically ill
conditioned, while the process estimation problem in the linear
case with appropriate assumptions leads to uniformly asymptotically
stable equations for the estimator and the gain. The conditions
relate to controlability and observability and will be detailed in
this volume. In the present volume, we present a series of lectures
on linear and nonlinear sequential filtering theory. The theory is
due to Kalman for the linear colored observation noise problem; in
the case of white observation noise it is the analog of the
continuous-time Kalman-Bucy theory. The discrete time filtering
theory requires only modest mathematical tools in counterpoint to
the continuous time theory and is aimed at a senior-level
undergraduate course. The present book, organized by lectures, is
actually based on a course that meets once a week for three hours,
with each meeting constituting a lecture."
This book is intended to be a comprehensive reference to
multiplicative com plexity theory as applied to digital signal
processing computations. Although a few algorithms are included to
illustrate the theory, I concentrated more on the develop ment of
the theory itself. Howie Johnson's infectious enthusiasm for
designing efficient DfT algorithms got me interested in this
subject. I am grateful to Prof. Sid Burrus for encouraging and
supporting me in this effort. I would also like to thank Henrik
Sorensen and Doug Jones for many stimulating discussions. lowe a
great debt to Shmuel Winograd, who, almost singlehandedly, provided
most of the key theoretical results that led to this present work.
His monograph, Arithmetic Complexity o/Computations, introduced me
to the mechanism behind the proofs of theorems in multiplicative
complexity. enabling me to return to his earlier papers and
appreciate the elegance of his methods for deriving the theory. The
second key work that influenced me was the paper by Louis Auslander
and Winograd on multiplicative complexity of semilinear systems
defined by polynomials. After reading this paper, it was clear to
me that this theory could be applied to many impor tant
computational problems. These influences can be easily discerned in
the present work.
Algorithms for computation are a central part of both digital
signal pro cessing and decoders for error-control codes and the
central algorithms of the two subjects share many similarities.
Each subject makes extensive use of the discrete Fourier transform,
of convolutions, and of algorithms for the inversion of Toeplitz
systems of equations. Digital signal processing is now an
established subject in its own right; it no longer needs to be
viewed as a digitized version of analog signal process ing.
Algebraic structures are becoming more important to its
development. Many of the techniques of digital signal processing
are valid in any algebraic field, although in most cases at least
part of the problem will naturally lie either in the real field or
the complex field because that is where the data originate. In
other cases the choice of field for computations may be up to the
algorithm designer, who usually chooses the real field or the
complex field because of familiarity with it or because it is
suitable for the particular application. Still, it is appropriate
to catalog the many algebraic fields in a way that is accessible to
students of digital signal processing, in hopes of stimulating new
applications to engineering tasks."
Radar, like most well developed areas, has its own vocabulary.
Words like Doppler frequency, pulse compression, mismatched filter,
carrier frequency, in-phase, and quadrature have specific meaning
to the radar engineer. In fact, the word radar is actually an
acronym for RAdio Detection And Rang ing. Even though these words
are well defined, they can act as road blocks which keep people
without a radar background from utilizing the large amount of data,
literature, and expertise within the radar community. This is
unfortunate because the use of digital radar processing techniques
has made possible the analysis of radar signals on many general
purpose digi tal computers. Of special interest are the surface
mapping radars, such as the Seasat and the shuttle imaging radars,
which utilize a technique known as synthetic aperture radar (SAR)
to create high resolution images (pic tures). This data appeals to
cartographers, agronomists, oceanographers, and others who want to
perform image enhancement, parameter estima tion, pattern
recognition, and other information extraction techniques on the
radar imagery. The first chapter presents the basics of radar
processing: techniques for calculating range (distance) by
measuring round trip propagation times for radar pulses. This is
the same technique that sightseers use when calculat ing the width
of a canyon by timing the round trip delay using echoes. In fact,
the corresponding approach in radar is usually called the pulse
echo technique."
This book is intended as an introduction to array signal process
ing, where the principal objectives are to make use of the
available multiple sensor information in an efficient manner to
detect and possi bly estimate the signals and their parameters
present in the scene. The advantages of using an array in place of
a single receiver have extended its applicability into many fields
including radar, sonar, com munications, astronomy, seismology and
ultrasonics. The primary emphasis here is to focus on the detection
problem and the estimation problem from a signal processing
viewpoint. Most of the contents are derived from readily available
sources in the literature, although a cer tain amount of original
material has been included. This book can be used both as a
graduate textbook and as a reference book for engineers and
researchers. The material presented here can be readily understood
by readers having a back ground in basic probability theory and
stochastic processes. A prelim inary course in detection and
estimation theory, though not essential, may make the reading easy.
In fact this book can be used in a one semester course following
probability theory and stochastic processes."
Convolution is the most important operation that describes the
behavior of a linear time-invariant dynamical system. Deconvolution
is the unraveling of convolution. It is the inverse problem of
generating the system's input from knowledge about the system's
output and dynamics. Deconvolution requires a careful balancing of
bandwidth and signal-to-noise ratio effects. Maximum-likelihood
deconvolution (MLD) is a design procedure that handles both
effects. It draws upon ideas from Maximum Likelihood, when unknown
parameters are random. It leads to linear and nonlinear signal
processors that provide high-resolution estimates of a system's
input. All aspects of MLD are described, from first principles in
this book. The purpose of this volume is to explain MLD as simply
as possible. To do this, the entire theory of MLD is presented in
terms of a convolutional signal generating model and some
relatively simple ideas from optimization theory. Earlier
approaches to MLD, which are couched in the language of
state-variable models and estimation theory, are unnecessary to
understand the essence of MLD. MLD is a model-based signal
processing procedure, because it is based on a signal model, namely
the convolutional model. The book focuses on three aspects of MLD:
(1) specification of a probability model for the system's measured
output; (2) determination of an appropriate likelihood function;
and (3) maximization of that likelihood function. Many practical
algorithms are obtained. Computational aspects of MLD are described
in great detail. Extensive simulations are provided, including real
data applications.
This book is dedicated to electrical and mechanical engineers
involved with the design of magnetic devices for motion con trol
and other instrumentation that uses magnetic principles and
technology. It can be of benefit to graduate and postgrad uate
students to gain experience with electro-magnetic princi ples and
also with different aspects of magnetic coupling mech anisms and
magnetic circuitry analysis for the design of devices such as
electrical servo motors, tachogenerators, encoders, gyro magnetic
suspension systems, electro-magnetic strip lines, and other
electro-magnetic instruments. The rapidly growing areas of
production automation, robotics, precise micro-electronics, and
pilot navigation place demands on motion control technology in
terms of accuracy, reliability, cost effectiveness, and
miniaturization. New ferromagnetic materials having quasi-linear
and non-linear high-squareness characteris tics as well as
high-energy permanent magnets, fine lithography, and
high-t.emperature superconductivit.y (t.o be expected com
mercially) motivate the implementation of new motion control
components that exploit these new materials and technologies. This
book presents classical miniature electrical machine de signs as
well as several modifications in the geometry of mag netic
couplings which lead to new motor and encoder design methodologies
and other motion control devices such as new coil deposition
patterns for incremental and absolute encoders, free spherical gyro
suspension in a traveling magnetic field for navigation
instrumentation, and magnetic strip lines in combi nation with
resistive and capacitive media to generate a variety of low-noise
LC filters and other signal processing devices."
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