---

Wavlet teorisini anlatan yaklaşık 50 sayfalık yararlı bir kaynak



WAVELETS
RONALD A. DeVORE and BRADLEY J. LUCIER
1. Introduction
The subject of \wavelets" is expanding at such a tremendous rate that it is
impossible to give, within these few pages, a complete introduction to all aspects of
its theory. We hope, however, to allow the reader to become suciently acquainted
with the subject to understand, in part, the enthusiasm of its proponents toward
its potential application to various numerical problems. Furthermore, we hope that
our exposition can guide the reader who wishes to make more serious excursions into
the subject. Our viewpoint is biased by our experience in approximation theory and
data compression; we warn the reader that there are other viewpoints that are either
not represented here or discussed only briefly. For example, orthogonal wavelets
were developed primarily in the context of signal processing, an application which
we touch on only indirectly. However, there are several good expositions (e.g.,
[Da1] and [RV]) of this application. A discussion of wavelet decompositions in
the context of Littlewood-Paley theory can be found in the monograph of Frazier,
Jawerth, and Weiss [FJW]. We shall also not attempt to give a complete discussion
of the history of wavelets. Historical accounts can be found in the book of Meyer
[Me] and the introduction of the article of Daubechies [Da1]. We shall try to give
enough historical commentary in the course of our presentation to provide some
feeling for the subject's development.
The term \wavelet" (originally called wavelet of constant shape) was introduced
by J. Morlet. It denotes a univariate function (multivariate wavelets exist as well
and will be discussed subsequently), dened on R, which, when subjected to the
fundamental operations of shifts (i.e., translation by integers) and dyadic dilation,
yields an orthogonal basis of L2(R). That is, the functions j;k := 2k=2 (2k
− j),
j; k 2 Z, form a complete orthonormal system for L2(R). In this work, we
shall call such a function an orthogonal wavelet, since there are many generalizations
of wavelets that drop the requirement of orthogonality. The Haar function
H := [0;1=2) − [1=2;1), which will be discussed in more detail in the section that
follows, is the simplest example of an orthogonal wavelet. Orthogonal wavelets with
higher smoothness (and even compact support) can also be constructed. But before
A version of this paper appeared in Acta Numerica, A. Iserles, ed., Cambridge University
Press, v. 1 (1992), pp. 1{56. This work was supported in part by the National Science Foundation
(grants DMS-8922154 and DMS-9006219), the Air Force Oce of Scientic Research (contract
89-0455-DEF), the Oce of Naval Research (contracts N00014-90-1343, N00014-91-J-1152, and
N00014-91-J-1076), the Defense Advanced Research Projects Agency (AFOSR contract 90-0323),
and the Army High Performance Computing Research Center at the University of Minnesota.


http://rapidshare.de/files/39768860/wavelet.rar.html

---

Başa dön