xviii
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PREFACE
theory. These fundamentals help the designer understand what it is that an adaptive filter is trying
to accomplish and how well it performs in
this
regard. For
this
reason, Parts
I
(Optimal
Estimation)
and
I
I
(Linear Estimation)
of
the
book are designed to provide the reader with a self-contained and
easy-to-follow exposition of estimation theory, with a focus on topics that are relevant to the subject
matter of the book. In these initial parts, special emphasis is placed on geometric interpretations of
several fundamental results.
The
reader is advised to pay close attention to these interpretations since
it will become clear, time and again, that cumbersome algebraic manipulations can often be simpli-
fied by recourse to geometric constructions. These constructions not only provide a more lasting
appreciation for the results of the book, but they also expose the reader to powerful tools that can be
useful in other contexts as well, other than adaptive filtering and estimation theory.
The reader is further advised to master the convenience of the vector notation, which is used
extensively throughout
this
book. Besides allowing a compact exposition of ideas and a compact
representation of results, the vector notation also allows
us
to exploit to great effect several important
results from linear algebra and matrix theory and to capture, in elegant ways, many revealing charac-
teristics of adaptive filters. We cannot emphasize strongly enough the importance
of
linear algebraic
and matrix tools in our presentation, as well as the elegance that they bring to the subject. The com-
bined power of the geometric point of view and the vector notation is perhaps best exemplified by our
detailed treatment later in
this
book of least-squares theory and its algorithmic variants.
Of
course,
the reader
is
exposed to geometric and vector formulations in the early chapters of the book.
STRUCTURE
OF
THE
BOOK
The book is divided into eleven core parts, in addition to a leading part on
Background Marerial
and
a trailing part on
References and Indices.
Table P.l lists the various parts. Each
of
the core parts,
numbered
I
through
XI,
consists of four distinctive elements in the following order: (i) a series of lec-
tures where the concepts are introduced, (ii) a
summary
of all lectures combined, (iii) bibliographic
commentary, and (iv) problems and computer projects.
Lectures and Concepts.
In the early parts of the book, each concept is motivated from first
principles; starting from the obvious and ending with the more advanced. We follow
this
route of
presentation until the reader develops enough maturity in the field.
As
the book progresses, we ex-
pect the reader to become more sophisticated and, therefore, we cut back on the “obvious.”
Summaries.
For ease of reference, at the end of each part, we collect a summary of the key con-
cepts and results introduced in the respective lectures.
Bibliographic Commentaries.
In the remarks at the end of each part we provide a wealth of
references
on
the main contributors to the results discussed in the respective lectures. Rather than
scatter references throughout the lectures, we find it useful to collect all references at the end of the
part in the form of a narrative. We believe that
this
way
of
presentation gives the reader a more
focused perspective on how
the
references and the contributions relate to each other both in time and
context.
Problems.
The book contains a significant number of problems, some more challenging than others
and some more applied than others. The problems should be viewed as an
integral
part of the text,
especially since additional results appear in them. It
is
for
this
reason, and also for the benefit of the
reader, that we have chosen to formulate and design most problems in a guided manner. Usually,
and especially in
the
more challenging cases, a problem
starts
by stating its objective followed by
a sequence
of
guided steps until the final answer
is
attained. In most cases, the answer to each
step appears stated in the body of the problem. In
this
way, a reader would know what the answer
should be, even if the reader fails to solve the problem. Thus rather than ask the reader to “find an
expression for
x,”,
we would generally ask instead to “show that
x
is given by
z
=
. .
.”
and then
give the expression for
x.
All
instructors can request copies
of
a
free
solutions manual from
the
publisher.
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