A Friendly Guide to Wavelets

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Springer Science & Business Media, Aug 1, 1994 - Mathematics - 300 pages
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This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption.

Chapters 10 and 11 consist of original research and are written in a more advanced style. In Chapter 10 it is shown that the structure of Maxwell's equations implies the existence of a wavelet analysis specifically adopted to electromagnetic radiation. The associated "eletromagnetic wavelets" are pulses parameterized by their point of origin and their scale, and can be made arbitrarily short by choosing fine scales. Furthermore, it is shown that every electromagnetic wave can be composed of such localized wavelets. This is applied in Chapter 11 to give a new formulation of radar based on electromagnetic wavelets. Since this theory is fully relativistic, its description of the Doppler effect is exact. In particular, it is three-dimensional, and does not make the usual assumption that the outgoing signal has a narrow bandwidth. Thus it should be useful in the construction of ultra-wideband radar systems.

 

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Contents

IV
3
V
12
VI
19
VII
26
VIII
34
IX
41
X
44
XII
50
XXXVIII
124
XXXIX
133
XL
137
XLI
139
XLIII
147
XLIV
160
XLV
169
XLVI
172

XIII
53
XIV
56
XV
58
XVI
60
XVIII
64
XIX
70
XX
73
XXI
77
XXII
78
XXIII
85
XXIV
88
XXV
89
XXVI
91
XXVII
95
XXVIII
96
XXIX
99
XXX
102
XXXI
104
XXXII
110
XXXIII
112
XXXIV
119
XXXV
121
XXXVI
123
XLVII
174
XLVIII
176
XLIX
183
L
189
LI
191
LII
197
LIV
203
LV
206
LVI
215
LVII
224
LVIII
229
LIX
233
LX
236
LXI
244
LXII
245
LXIV
256
LXV
271
LXVII
275
LXVIII
281
LXIX
283
LXX
291
LXXI
297
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