Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications (Ultrasound in Biomedicine Research
Signal analysis gives an insight into the properties of signals and stochastic processes by methodology. Linear transforms are integral to the continuing growth of signal processes as they characterize and classify signals. In particular, those transforms that provide time--frequency signal analysis are attracting greater numbers of researchers and are becoming an area of considerable importance. The key characteristic of these transforms, along with a certain time--frequency localization called the wavelet transform and various types of multirate filter banks, is their high computational efficiency. It is this computational efficiently which accounts for their increased application. This book provides a complete overview and introduction to signal analysis. It presents classical and modern signal analysis methods in a sequential structure starting with the background to signal theory. Progressing through the book the author introduces more advanced topics in an easy to understand style. Including recent and emerging topics such as filter banks with perfect reconstruction, time frequency and wavelets. With great accuracy and technical merit, this book makes a useful and original contribution to the current literature.
Why Read This Book
You should read this book if you want a unified, engineering-oriented treatment of wavelet theory, multirate filter banks, and time–frequency transforms that bridges mathematical foundations and practical algorithms. It explains design principles and efficient implementations and shows how those tools are applied to real signal-processing problems such as denoising, compression, and spectral analysis.
Who Will Benefit
Graduate students and practicing engineers working on signal analysis, filter-bank design, compression or time–frequency methods who need both theory and practical design guidance.
Level: Advanced — Prerequisites: Solid linear systems and signals background, familiarity with Fourier transforms and linear algebra; some exposure to probability and stochastic processes is helpful.
Key Takeaways
- Explain the mathematical foundations of continuous and discrete wavelet transforms and their time-frequency localization properties.
- Design and analyze critically sampled and oversampled multirate filter banks including perfect-reconstruction conditions.
- Derive and implement efficient algorithms for fast wavelet and subband transforms.
- Apply time–frequency representations (STFT, Wigner, wavelets) to tasks such as denoising, detection and compression.
- Evaluate trade-offs between orthogonal and biorthogonal constructions and choose filter prototypes for target applications.
Topics Covered
- Introduction and motivation for time–frequency analysis
- Basic properties of signals and stochastic processes
- Short-time Fourier transform and spectrograms
- Quadratic time–frequency distributions (Wigner–Ville and Cohen class)
- Continuous wavelet transform and time–scale analysis
- Discrete wavelet transform and multiresolution analysis
- Multirate signal processing and filter-bank fundamentals
- Perfect-reconstruction filter banks: orthogonal and biorthogonal designs
- Design methods for wavelet and subband filters
- Fast algorithms and efficient implementations
- Applications: denoising, compression, feature extraction
- Practical considerations and numerical examples
Languages, Platforms & Tools
How It Compares
Covers largely the same engineering ground as Vetterli & Kovacevic's 'Wavelets and Subband Coding' but with broader time–frequency material; less tutorial/visual than Mallat's 'A Wavelet Tour of Signal Processing' but more focused on filter-bank design and computational aspects.
