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[资源] Wavelet and Subband Coding 英文版本,外加小波入门学习英文版

Wavelets and Subband Coding
Martin Vetterli
University of California at Berkeley
Jelena Kovaˇcevi´c
AT&T Bell Laboratories

Contents
Preface xiii
1 Wavelets, Filter Banks and Multiresolution Signal Processing 1
1.1 Series Expansions of Signals .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    3
1.2 Multiresolution Concept  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    9
1.3 Overview of the Book .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 10
2 Fundamentals of Signal Decompositions 15
2.1 Notations .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 16
2.2 Hilbert Spaces .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 17
2.2.1 Vector Spaces and Inner Products .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 18
2.2.2 Complete Inner Product Spaces .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 21
2.2.3 Orthonormal Bases .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 23
2.2.4 General Bases .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 27
2.2.5 Overcomplete Expansions  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 28
2.3 Elements of Linear Algebra .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 29
2.3.1 Basic Deﬁnitions and Properties .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 30
2.3.2 Linear Systems of Equations and Least Squares .  .  .  .  .  .  .  . 32
2.3.3 Eigenvectors and Eigenvalues  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 33
2.3.4 Unitary Matrices  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 34
2.3.5 Special Matrices .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 35
2.3.6 Polynomial Matrices  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 36
2.4 Fourier Theory and Sampling  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 37
vii
......

1
Wavelets, Filter Banks and Multiresolution
Signal Processing
“It is with logic that one proves;
it is with intuition that one invents.”
— Henri Poincar´e
The topic of this book is very old and very new.  Fourier series, or expansion of
periodic functions in terms of harmonic sines and cosines, date back to the early
part of the 19th century when Fourier proposed harmonic trigonometric series [100].
The ﬁrst wavelet (the only example for a long time!)  was found by Haar early in
this century [126].  But the construction of more general wavelets to form bases
for square-integrable functions was investigated in the 1980’s, along with eﬃcient
algorithms to compute the expansion. At the same time,  applications  of these
techniques in signal processing have blossomed.
While linear expansions of functions are a classic subject, the recent construc-
tions contain interesting new features. For example, wavelets allow good resolution
in time and frequency, and should thus allow one to see “the forest and the trees.”
This feature is important for nonstationary signal analysis. While Fourier basis
functions are given in closed form, many wavelets can only be obtained through a
computational procedure (and even then, only at speciﬁc rational points).  While
this might seem to be a drawback, it turns out that if one is interested in imple-
menting a signal expansion on real data, then a computational procedure is better
than a closed-form expression!

..................[ Last edited by nmwhx001 on 2013-2-5 at 00:23 ]

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