Most existing books on wavelets are either too mathematical or they focus on too narrow a specialty. This book provides a thorough treatment of the subject from an engineering point of view. It is a one-stop source of theory, algorithms, applications, and computer codes related to wavelets. This second edition has been updated by the addition of:
- a section on Other Wavelets that describes curvelets, ridgelets, lifting wavelets, etc
- a section on lifting algorithms
- Sections on Edge Detection and Geophysical Applications
- Section on Multiresolution Time Domain Method (MRTD) and on Inverse problems
1.What is this book all about?
2. Mathematical Preliminary.
2.1 Linear Spaces.
2.2 Vectors and Vector Spaces.
2.3 Basis Functions, Orthogonality and Biothogonality.
2.4 Local Basis and Riesz Basis.
2.5 Discrete Linear Normed Space.
2.6 Approximation by Orthogonal Projection.
2.7 Matrix Algebra and Linear Transformation.
2.8 Digital Signals.
2.9 Exercises.
2.10 References.
3. Fourier Analysis.
3.1 Fourier Series.
3.2 Rectified Sine Wave.
3.3 Fourier Transform.
3.4 Properties of Fourier Transform.
3.5 Examples of Fourier Transform.
3.6 Poisson’s Sum and Partition of ZUnity.
3.7 Sampling Theorem.
3.8 Partial Sum and Gibb’s Phenomenon.
3.9 Fourier Analysis of Discrete-Time Signals.
3.10 Discrete Fourier Transform (DFT).
3.11 Exercise.
3.12 References.
4. Time-Frequency Analysis.
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