文档介绍：More Mathematical Methods and Algorithms For
Signal Processing
V.
Todd K. Moon
Utah State University
May 15, 2000
Preface
Why this book?
More Mathematical Methods and Algorithms is intended (eventually) to serve the same
vision as the original Methods: to provide a useful and thorough foundation in mathematics
that will help the signal processor understand and develop effective algorithms. In fact, the
material in this book was intended to be part of the original Methods, but was jettisoned as
the other exceeded reasonable bounds.
This material has not yet been edited, proofread, revised, and vetted. It is a certainty
that errors remain: read it with scepticism. Also, it is not yet in any plete. There
is new material I would eventually like to include. For example, closely associated with
the concept of interpolation, but tying in the Euclidean algorithm in a potent way, is the
method of lifting for wavelet transforms. This will ultimately be worked in.
I hope that even in its present form the material serves some benefit, which is why I am
making it available on the . If you care ment on the material — particularly
to point out errors and suggestions for improvement — please do so.
— .
iv Preface
Contents
Preface iii
I Number Theoretic Methods 1
1 Some number theory and its applications 3
Introduction .................................. 3
Divisibility and the Euclidean algorithm ................... 4
Some applications of the Euclidean algorithm . ........... 9
mon multiples . . . . ................... 11
Exercises . .................................. 11
Congruences and remainders . . . . . . ................... 13
Properties of the
function and an application ........... 18
Polynomials evaluation and congruences . . . ........... 20
Exercises . .................................. 21
Solution of linear congruences . . . . . ................... 23
Exer