Sampling Theory

Yonina C. Eldar is a Professor in the Department of Electrical Engineering at the Technion – Israel Institute of Technology (holding the Edwards Chair in Engineering), a Research Affiliate with the Research Laboratory of Electronics at the Massachusetts Institute of Technology and a Visiting Professor at Stanford University. She has received numerous awards for excellence in research and teaching, including the Wolf Foundation Krill Prize for Excellence in Scientific Research, the Hershel Rich Innovation Award, the Michael Bruno Memorial Award from the Rothschild Foundation, the Weismann Prize for Exact Sciences, and the Muriel and David Jacknow Award for Excellence in Teaching. She is the Editor in Chief of Foundations and Trends in Signal Processing and an Associate Editor for several journals in the areas of signal processing and mathematics. She is a Signal Processing Distinguished Lecturer, an IEEE Fellow, a member of the Young Israel Academy of Science and the Israel Committee for Higher Education.

'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

• 1. 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.