Adapted Wavelet Analysis: From Theory to Software
This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficients
Why Read This Book
You should read this book if you need a practical, implementation-minded bridge between wavelet theory and working software — it walks through transforms, filter constructions, wavelet packets and the best-basis algorithm with programming tips. You will gain concrete guidance for turning wavelet ideas into reliable analysis code for real signals.
Who Will Benefit
Engineers or applied mathematicians who write signal-processing software and need hands-on guidance implementing wavelet transforms, wavelet packets and best-basis selection for analysis tasks.
Level: Advanced — Prerequisites: Familiarity with linear algebra, Fourier analysis, basic DSP concepts (filters, transforms) and experience programming (MATLAB/C or equivalent).
Key Takeaways
- Implement the discrete wavelet transform (DWT) and construct quadrature mirror filters for practical use
- Apply and code wavelet packet decompositions and navigate their tree structures
- Implement the Best Basis algorithm to select data-adaptive bases for time-frequency representation
- Perform time-frequency and local trigonometric analyses using library-tree frameworks
- Design and adapt multidimensional library trees for image/volume data and other higher-dimensional signals
- Integrate mathematical foundations into robust, production-oriented software for real-data analysis
Topics Covered
- Mathematical Preliminaries
- Programming Techniques
- The Discrete Fourier Transform
- Local Trigonometric Transforms
- Quadrature Filters
- The Discrete Wavelet Transform
- Wavelet Packets
- The Best Basis Algorithm
- Multidimensional Library Trees
- Time-Frequency Analysis
- Some Applications
- Solutions to Some of the Exercises
- List of Symbols
- Quadrature Filter Coefficients
Languages, Platforms & Tools
How It Compares
More implementation-focused than Mallat's 'A Wavelet Tour of Signal Processing' and more algorithmic/practical than Daubechies' 'Ten Lectures on Wavelets' — Wickerhauser emphasizes wavelet packets and best-basis programming details.
