Modern Sampling Theory
A state-of-the-art edited survey covering all aspects of sampling theory. Theory, methods and applications are discussed in authoritative expositions ranging from multi-dimensional signal analysis to wavelet transforms. The book is an essential up-to-date resource.
Why Read This Book
You should read this book if you need a rigorous, comprehensive treatment of modern sampling theory that connects classical Shannon results to contemporary frameworks such as frames, shift-invariant spaces and wavelet-based reconstruction. It gives you authoritative surveys and proofs that clarify when and how exact reconstruction is possible beyond uniform bandlimited models.
Who Will Benefit
Graduate students, researchers, and senior DSP engineers who design sampling/reconstruction schemes, multirate filterbanks, or study theoretical foundations of wavelets and frames.
Level: Advanced — Prerequisites: Undergraduate signals & systems and linear algebra; solid familiarity with Fourier transforms, basic functional analysis (Hilbert spaces) and some complex-variable or distribution theory will help greatly.
Key Takeaways
- Understand the mathematical generalizations of the Shannon sampling theorem including nonuniform and multivariate sampling.
- Explain the role of frames and Riesz bases in stable signal reconstruction and design sampling sets in shift-invariant spaces.
- Apply wavelet and multirate concepts to sampling and reconstruction problems for localized and multi-scale signals.
- Analyze conditions for perfect reconstruction and robustness to jitter or missing samples in practical systems.
- Relate sampling theory results to practical constructs such as filterbanks and interpolation algorithms.
Topics Covered
- Introduction and historical overview of sampling theory
- Classical Shannon sampling and bandlimited signals
- Nonuniform sampling: interpolation and reconstruction
- Frames, Riesz bases, and stable reconstruction
- Sampling in shift-invariant and spline spaces
- Multidimensional and multivariate sampling
- Connections between sampling and wavelet theory
- Multirate filterbanks and sampling applications
- Numerical methods, algorithms and stability analysis
- Applications and open problems in modern sampling
How It Compares
Covers similar rigorous, theory-focused ground as Marvasti's Nonuniform Sampling collection but with stronger emphasis on frames and wavelet connections; more mathematical than Mallat's A Wavelet Tour of Signal Processing, which is more applied and algorithm-focused.
