A First Course in Wavelets with Fourier Analysis by Albert Boggess

By Albert Boggess

A entire, self-contained remedy of Fourier research and wavelets—now in a brand new edition
Through expansive insurance and easy-to-follow reasons, a primary direction in Wavelets with Fourier research, moment variation offers a self-contained mathematical therapy of Fourier research and wavelets, whereas uniquely proposing sign research functions and difficulties. crucial and primary principles are provided so one can make the e-book available to a vast viewers, and, additionally, their functions to sign processing are stored at an straight forward level.

The publication starts off with an creation to vector areas, internal product areas, and different initial themes in research. next chapters feature:

The improvement of a Fourier sequence, Fourier rework, and discrete Fourier analysis

Improved sections dedicated to non-stop wavelets and two-dimensional wavelets

The research of Haar, Shannon, and linear spline wavelets

The normal concept of multi-resolution analysis

Updated MATLAB code and accelerated functions to sign processing

The building, smoothness, and computation of Daubechies' wavelets

Advanced themes reminiscent of wavelets in larger dimensions, decomposition and reconstruction, and wavelet transform

Applications to sign processing are supplied during the ebook, so much regarding the filtering and compression of signs from audio or video. a few of these functions are offered first within the context of Fourier research and are later explored within the chapters on wavelets. New workouts introduce extra functions, and entire proofs accompany the dialogue of every offered concept. broad appendices define extra complicated proofs and partial ideas to routines in addition to up-to-date MATLAB workouts that complement the offered examples.

A First path in Wavelets with Fourier research, moment variation is a superb ebook for classes in arithmetic and engineering on the upper-undergraduate and graduate degrees. it's also a worthy source for mathematicians, sign processing engineers, and scientists who desire to know about wavelet conception and Fourier research on an basic level.

Table of Contents

Preface and Overview.
0 internal Product Spaces.

0.1 Motivation.

0.2 Definition of internal Product.

0.3 The areas L2 and l2.

0.4 Schwarz and Triangle Inequalities.

0.5 Orthogonality.

0.6 Linear Operators and Their Adjoints.

0.7 Least Squares and Linear Predictive Coding.

Exercises.

1 Fourier Series.

1.1 Introduction.

1.2 Computation of Fourier Series.

1.3 Convergence Theorems for Fourier Series.

Exercises.

2 The Fourier Transform.

2.1 casual improvement of the Fourier Transform.

2.2 homes of the Fourier Transform.

2.3 Linear Filters.

2.4 The Sampling Theorem.

2.5 The Uncertainty Principle.

Exercises.

3 Discrete Fourier Analysis.

3.1 The Discrete Fourier Transform.

3.2 Discrete Signals.

3.3 Discrete indications & Matlab.

Exercises.

4 Haar Wavelet Analysis.

4.1 Why Wavelets?

4.2 Haar Wavelets.

4.3 Haar Decomposition and Reconstruction Algorithms.

4.4 Summary.

Exercises.

5 Multiresolution Analysis.

5.1 The Multiresolution Framework.

5.2 imposing Decomposition and Reconstruction.

5.3 Fourier remodel Criteria.

Exercises.

6 The Daubechies Wavelets.

6.1 Daubechies’ Construction.

6.2 category, Moments, and Smoothness.

6.3 Computational Issues.

6.4 The Scaling functionality at Dyadic Points.

Exercises.

7 different Wavelet Topics.

7.1 Computational Complexity.

7.2 Wavelets in better Dimensions.

7.3 bearing on Decomposition and Reconstruction.

7.4 Wavelet Transform.

Appendix A: Technical Matters.

Appendix B: options to chose Exercises.

Appendix C: MATLAB® Routines.

Bibliography.

Index.

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