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Kaiser D. — A Friendly Guide to Wavelets
Kaiser D. — A Friendly Guide to Wavelets

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Название: A Friendly Guide to Wavelets

Автор: Kaiser D.

Аннотация:

This volume consists of two parts. Chapters 1-8, Basic Wavelet Analysis, are aimed at graduate students or advanced undergraduates in science, engineering, and mathematics. They are designed for an introductory one-semester course on wavelets and time frequency analysis, and can also be used for self-study or reference by practicing researchers in signal analysis and related areas. The reader is not presumed to have a sophisticated mathematical background; therefore, much of the needed analytical machinery is developed from the beginning. The only prerequisite is a knowledge of matrix theory, Fourier series, and Fourier integral transforms. Notation is introduced which facilitates the formulation of signal analysis in a modern and general mathematical language, and the illustrations should further ease comprehension. Each chapter ends with a set of straightforward exercises designed to drive home the concepts.
Chapters 9-11, Physical Wavelets, are at a more advanced level and represent original research. They can be used as a text for a second-semester course or, when combined with Chapters 1 and 3, as a reference for a research seminar. Whereas the wavelets of Part I can be any functions of "time," physical wavelets are functions of space-time constrained by differential equations. In Chapter 9, wavelets specifically dedicated to Maxwell's equations are constructed. These wavelets are electromagnetic pulses parameterized by their point and time of emission or absorption, their duration, and the velocity of the emitter or absorber. The duration also acts as a scale parameter. We show that every electromagnetic wave can be composed from such wavelets. This fact is used in Chapter 10 to give a new formulation of electromagnetic imaging, such as radar, accompanied by a geometrical model for scattering based on conformal transformations. In Chapter 11, a similar set of wavelets is developed for acoustics. A relation is established at the fundamental level of differential equations between physical waves and time signals. This gives a one-to-one correspondence between physical wavelets and a particular family of time wavelets.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1994

Количество страниц: 300

Добавлена в каталог: 05.12.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accelerating reference frame      212 244
Acoustic wavelets      273
Acoustic wavelets, absorbed      278
Acoustic wavelets, emitted      278
Adjoint      13 24-25
Admissibility condition      67
Admissible      264
Affine group      205 257
Affine transformations      257
Aliasing operator      162
Almost everywhere (a.e.)      22
Ambiguity function      250 254
Ambiguity function, conformal cross      266
Ambiguity function, conformal self      266
Ambiguity function, narrow-band      254
Ambiguity function, narrow-band cross      254
Ambiguity function, narrow-band self      254
Ambiguity function, wide-band      248
Ambiguity function, wide-band cross      250
Ambiguity function, wide-band self      250
Analytic signal      68 206 218 219
Analytic signal, lower      73
Analytic signal, upper      73
Analyzing operator      83
Antilinear      12
Atomic composition      233
Averaging operator      142
Averaging property      141
Balian - Low theorem      116
Band-limited      99
Bandwidth      99 252
Basis      4
Basis, dual      9
Basis, reciprocal      16
Bernstein's inequality      101
Biorthogonal      15
Blurring      144 242
Bounded      26
Bounded, linear functional      27
Bra      14
Carrier frequency      252
Causal      205
Causal cone      222
Causal tube      206 223
Characteristic function      40
Chirp      47
complete      4 80
Complex space-time      206
Complex structure      207
Conformal cross-ambiguity function      250 254 266
Conformal group      204
Conformal self-ambiguity function      266
Conformal transformations      260
Conformal transformations, special      260 269
Consistency condition      57 87 234 249
Counting measure      40 106
Cross-ambiguity function      250 254
Cumulants      191-196
De-aliasing operator      163 164
Dedicated wavelets      204
Demodulation      253
detail      63
Diadic interpolation      189
Diadic rationals      188 190
Differencing operator      152
Dilation equation      142
Dirac notation      14
distribution      26
Doppler effect      243 247
Doppler shift      252
Down-sampling operator      149
Duality relation      9
Duration      206 242
Electromagnetic wavelets      224
Elementary current      279
Elementary scatterers      263
Elementary scattering event      265
Euclidean region      225
Evaluation map      224
Exact scaling functions      191
Filter coefficients      142
Filter extremal-phase      181
Filter linear-phase      181
Filter maximum-phase      181
Filter minimum-phase      181
Finite impulse response (FIR)      155 176
Focal point      205
Fourier coefficients      27
Fourier series      26
Fourier transform      29
Fractal      183
Frame      82
Frame, bounds      82
Frame, condition      82
Frame, deformations of      117-218
Frame, discrete      82 91
Frame, generalized      82
Frame, normalized      83
Frame, operator      83
Frame, reciprocal      86
Frame, snug      90
Frame, tight      82
Frame, vectors      82
Future cone      222
Gabor expansions      114
Gauge freedom      212
H$\ddot{o}$lder, continuous      187-188
H$\ddot{o}$lder, exponents      188
Haar wavelet      159
harmonic oscillator      118
Helicity      206 210
High-pass filter      147
High-pass filter sequence      154
Hilbert space      23
Hilbert transform      251 252
Hyperbolic lattice      124
Ideal band-pass filter      167
Ideal low-pass filter      110
Identity operator      10
Image      6
incomplete      4
Inner product      12
Inner product, standard      12
Instantaneous frequency      47
Interpolation operator      148
Inverse Fourier transform      33
Inverse image      36
Inverse problem      248
Isometry      69
Isometry, partial      69
Ket      14
Kronecker delta      5
Least-energy representation      101
Least-squares approximation      88
Lebesgue integral      21
Lebesgue measure      35
Light cone      208
Linear      6
Linear functional      24
Linear functional, bounded      24
Linearly dependent      4 80
Linearly independent      4
Lipschitz continuous      187
Lorentz condition      211
Lorentz group      259
Lorentz invariant inner product      208
Lorentz transformations      237
Low-pass filter      147
Massless Sobolev space      216
Matching      248
Maxwell's equations      207
Mean time      191
Measurable      21 35
Measure      21 35
Measure, space      40
Measure, zero      22
Metric operator      18
Mexican hat      75
Meyer wavelets      167
Moments      193
Multiresolution analysis      144
N      241
Narrow-band signal      252
Negative-frequency cone      222
Nondiffracting beams      272
Norm      12
Numerically stable      104
Nyquist rate      101
Operator      23
Operator, bounded      23
Orthogonal      13
Orthonormal      13
Oscillation      273
Over complete      4
Oversampling      88 101
Parseval's identity      33
Past cone      222
Periodic      26
Plancherel's Theorem      29 32
Plane waves      206
Poincar$\acute{e}$ group      259
Polarization identity      33
Positive-definite operators      18
Potentials      211
Proxies      246 256 280
Quadrature mirror filters      148
Quaternionic structure      171
RANGE      245
Ray filter      243
Redundancy      108
Reference wavelet      239 240
Reflectivity distribution      248
Reflector, complex      267
Reflector, elementary      263
Reflector, standard      263
Regular lattice      117
Representation      206 261
Reproducing kernel      70 228-233
Resolution      145
Resolution of unity      10
Resolution of unity, continuous      55
Rest frame      281-283
Riesz representation theorem      24
Sampling      92 99
Sampling operator      161
Sampling rate      101
Scale factor      63
Scaling function      140
Scaling invariant      126
Scaling periodic      127
Schwarz inequality      18 23
Shannon sampling theorem      99
Shannon wavelets      167
Space-time domain      31
Space-time inversion      260
span      9
Special conformal transformations      212
Spectral factorization      180
square-integrable      23
Square-summable      20
Stability      243
Stability condition      128
Star notation      17
Subband      111
Subband filtering      153-155
subspace      4
Support      23
Support, compact      23
Synthesizing operator      85 236
Time-limited      102
Transform, analytic-signal      218
Triangle inequality      18 23
Trigonometric polynomial      143
Tube, causal      206 223
Tube, future      223
Tube, past      223
Uncertainty principle      52
Up-sampling operator      148
Vector space      4
Vector space, complex      4
Vector space, real      4
Wave equation      207 272
Wave number-frequency domain      31
Wave vector      30
Wavelet      62
Wavelet, basic      62
Wavelet, mother      62
Wavelet, packets      172
Wavelet, space      236
Weyl - Heisenberg group      51 205
Window      45
Zak transform      117
Zero moments      178
Zoom operators      148
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