Sampling Theory

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. 'I must say that this is really a unique book on sampling theory. The introduction of vector space terminology right from the beginning is a great idea. Starting from classical sampling, the book goes all the way to the most recent breakthroughs including compressive sensing, union-of-subspace setting, and the CoSamp algorithm. Eldar has the right combination of mathematics and practical sense, and she has very good command of the 'art of writing'. This, combined with the archival nature of the topic (which has seen seven decades of history), makes the book an invaluable addition to the Cambridge collection of advanced texts in signal processing.' P. P. Vaidyanathan, California Institute of Technology 'The observation that a bandlimited signal is completely specified by uniform sampling at Nyquist rate might well go back to Cauchy, and the idea of approaching signal recovery as parameter estimation certainly goes back to the 1950s. These ideas provided the theoretical foundation for digitization of telephone networks and in turn the challenge of digital communication inspired new developments in signal analysis. Today new applications from A/D conversion to medical imaging are inspiring a new sampling theory and this book takes us to terra incognita beyond bandlimited systems.' Robert Calderbank, Duke University1. Introduction; 2. Introduction to linear algebra; 3. Fourier analysis; 4. Signal spaces; 5. Shift-invariant spaces; 6. Subspace priors; 7. Smoothness priors; 8. Nonlinear sampling; 9. Resampling; 10. Unions of subspaces; 11. Compressed sensing; 12. Sampling over finite unions; 13. Sampling over shift-invariant unions; 14. Multiband sampling; 15. Finite rate of innovation sampling; Appendix A. Finite linear algebra; Appendix B. Stochastic signals.