Sampling Theory: Beyond Bandlimited Systems
Covering the fundamental mathematical underpinnings together with key principles and applications, this book provides a comprehensive guide to the theory and practice of sampling from an engineering perspective. Beginning with traditional ideas such as uniform sampling in shift-invariant spaces and working through to the more recent fields of compressed sensing and sub-Nyquist sampling, the key concepts are addressed in a unified and coherent way. Emphasis is given to applications in signal processing and communications, as well as hardware considerations, throughout. With 200 worked examples and over 200 end-of-chapter problems, this is an ideal course textbook for senior undergraduate and graduate students. It is also an invaluable reference or self-study guide for engineers and students across industry and academia.
Why Read This Book
You will gain a unified, engineering‑oriented understanding of sampling that goes well beyond the classical bandlimited paradigm, learning both the rigorous mathematics and practical methods for modern sub‑Nyquist and sparse sampling systems. The book ties theory to applications — from communications and radar to audio and ADC hardware — with hundreds of worked examples and problems so you can apply the ideas to real systems.
Who Will Benefit
Senior undergraduates, graduate students, and practicing engineers in signal processing, communications, radar, and instrumentation who need to design or analyze sampling systems beyond the Nyquist/bandlimited assumption.
Level: Advanced — Prerequisites: Undergraduate-level signals and systems (Fourier transforms, sampling theorem), linear algebra, basic probability and estimation, and familiarity with digital signal processing concepts; calculus and some functional analysis exposure is helpful.
Key Takeaways
- Understand the mathematical foundations of sampling in Hilbert spaces, frames, and shift‑invariant spaces.
- Apply generalized sampling and reconstruction techniques to non‑bandlimited signals and finite‑rate‑of‑innovation (FRI) models.
- Design and analyze compressed sensing and sub‑Nyquist sampling strategies for sparse and structured signals.
- Evaluate practical hardware and ADC architectures that enable sub‑Nyquist acquisition, including multichannel and modulated sampling schemes.
- Implement numerical reconstruction algorithms and assess performance in noisy and statistical settings.
Topics Covered
- 1. Introduction and overview of classical sampling
- 2. Mathematical preliminaries: Hilbert spaces, frames, and Riesz bases
- 3. Shift‑invariant spaces and sampling in SI systems
- 4. Generalized sampling and reconstruction methods
- 5. Multirate systems, filter banks, and multichannel sampling
- 6. Finite‑Rate‑of‑Innovation (FRI) signals and their sampling
- 7. Sampling in unions of subspaces and structured signal models
- 8. Compressed sensing theory and sparse sampling for analog signals
- 9. Sub‑Nyquist sampling architectures and practical implementations
- 10. Noise, statistical estimation, and performance analysis
- 11. Applications: communications, radar, audio/speech, and imaging
- 12. Numerical methods, worked examples, and end‑of‑chapter problems
Languages, Platforms & Tools
How It Compares
Covers similar foundational material to Vetterli, Kovacević & Goyal's "Foundations of Signal Processing" but focuses more deeply on sampling beyond bandlimited signals, practical sub‑Nyquist architectures, and links to compressed sensing; complements Papoulis' classic work on generalized sampling with modern sparse‑signal perspectives.
