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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:

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
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 Hlder, continuous      187-188 Hlder, 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 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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