موجک‌ها: آموزشی در نظریه و کاربردها (تحلیل موجک و کاربردهای آن، جلد دوم)

Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume. Key Features * Covers several of the most important areas in wavelets, ranging from the development of the basic theory, such as: * Construction and analysis of wavelet bases, and * Introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding * Extensive bibliography is also included in this volume * Companion to the first volume in this series, An Introduction to Wavelets, and can be used as supplementary instructional material for a two-semester course on wavelet analysis Content: Wavelet Analysis and Its Applications , Page ii Front Matter , Page iii Copyright , Page iv Preface , Pages vii-x Daubechies' xfScaling Function on [0, 3] , Pages 3-13 Wavelet Matrices and the Representation of Discrete Functions , Pages 15-50 Wavelets and Generalized Functions , Pages 51-70 Cardinal Spline Interpolation and the Block Spin Construction of Wavelets , Pages 73-90 Polynomial Splines and Wavelets-A Signal Processing Perspective , Pages 91-122 Biorthogonal Wavelets , Pages 123-152 Nonorthogonal Multiresolution Analysis Using Wavelets , Pages 153-178 Wavelets and Other Bases for Fast Numerical Linear Algebra , Pages 181-216 Wavelets with Boundary Conditions on the Interval , Pages 217-236 Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets , Pages 237-256 Some Elementary Properties of Multiresolution Analyses of L 2 ( R n ) , Pages 259-294 Multidimensional Two–Scale Dilation Equations , Pages 295-323 Multivariate Wavelets , Pages 325-355 Gabor Wavelets and the Heisenberg Group: Gabor Expansions and Short Time Fourier Transform from the Group Theoretical Point of View , Pages 359-397 Windowed Radon Transforms, Analytic Signals, and the Wave Equation , Pages 399-441 Irregular Sampling and Frames , Pages 445-507 Families of Wavelet Transforms in Connection with Shannon's Sampling Theory and the Gabor Transform , Pages 509-528 Wavelets in H 2 (R): Sampling, Interpolation, and Phase Space Density , Pages 529-540 Orthonormal Wavelets, Analysis of Operators, and Applications to Numerical Analysis , Pages 543-601 Wavelet Transforms and Filter Banks , Pages 603-654 Second Generation Compact Image Coding with Wavelets , Pages 655-678 Acoustic Signal Compression with Wavelet Packets , Pages 679-700 Bibliography , Pages 701-713 Subject Index , Pages 715,717-723 WAVELET ANALYSIS AND ITS APPLICATIONS , Page 725 A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume. Key Features * Covers several of the most important areas in wavelets, ranging from the development of the basic theory, such * Construction and analysis of wavelet bases, and * Introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding * Extensive bibliography is also included in this volume * Companion to the first volume in this series, An Introduction to Wavelets, and can be used as supplementary instructional material for a two-semester course on wavelet analysis We construct Daubechies' scaling function supported on [0,3] from first principles and prove that it is continuous everywhere, left-differentiable at dyadic rationals and nowhere right-differentiable on dyadic rationals on [0,3].