Foundations of Signal Processing

This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

1. On rainbows and spectra; 2. From Euclid to Hilbert: 2.1 Introduction; 2.2 Vector spaces; 2.3 Hilbert spaces; 2.4 Approximations, projections, and decompositions; 2.5 Bases and frames; 2.6 Computational aspects; 2.A Elements of analysis and topology; 2.B Elements of linear algebra; 2.C Elements of probability; 2.D Basis concepts; Exercises with solutions; Exercises; 3. Sequences and discrete-time systems: 3.1 Introduction; 3.2 Sequences; 3.3 Systems; 3.4 Discrete-time Fourier Transform; 3.5 z-Transform; 3.6 Discrete Fourier Transform; 3.7 Multirate sequences and systems; 3.8 Stochastic processes and systems; 3.9 Computational aspects; 3.A Elements of analysis; 3.B Elements of algebra; Exercises with solutions; Exercises; 4. Functions and continuous-time systems: 4.1 Introduction; 4.2 Functions; 4.3 Systems; 4.4 Fourier Transform; 4.5 Fourier series; 4.6 Stochastic processes and systems; Exercises with solutions; Exercises; 5. Sampling and interpolation: 5.1 Introduction; 5.2 Finite-dimensional vectors; 5.3 Sequences; 5.4 Functions; 5.5 Periodic functions; 5.6 Computational aspects; Exercises with solutions; Exercises; 6. Approximation and compression: 6.1 Introduction; 6.2 Approximation of functions on finite intervals by polynomials; 6.3 Approximation of functions by splines; 6.4 Approximation of functions and sequences by series truncation; 6.5 Compression; 6.6 Computational aspects; Exercises with solutions; Exercises; 7. Localization and uncertainty: 7.1 Introduction; 7.2 Localization for functions; 7.3 Localization for sequences; 7.4 Tiling the time–frequency plane; 7.5 Examples of local Fourier and wavelet bases; 7.6 Recap and a glimpse forward; Exercises with solutions; Exercises.

Martin Vetterli is a Professor of Computer and Communication Sciences at the École Polytechnique Fédérale de Lausanne, and the President of the Swiss National Science Foundation. He has formerly held positions at Columbia University and the University of California, Berkeley, and has received the IEEE Signal Processing Society Technical Achievement Award (2001) and Society Award (2010). He is a Fellow of the ACM, EURASIP and the IEEE, and is a Thomson Reuters Highly Cited Researcher in Engineering.
Jelena Kovacevic is the David Edward Schramm Professor and Head of Electrical and Computer Engineering, and a Professor of Biomedical Engineering, at Carnegie Mellon University. She has been awarded the Belgrade October Prize (1986), the E. I. Jury Award (1991) from Columbia University, and the 2010 Philip L. Dowd Fellowship at Carnegie Mellon University. She is a former Editor-in-Chief of IEEE Transactions on Image Processing, and a Fellow of the IEEE.
Vivek K Goyal is an Assistant Professor of Electrical and Computer Engineering at Boston University, and a former Esther and Harold E. Edgerton Associate Professor of Electrical Engineering at the Massachusetts Institute of Technology. He has been awarded the IEEE Signal Processing Society Magazine Award (2002), and the Eliahu Jury Award (1998) from the University of California, Berkeley, for outstanding achievement in systems, communications, control and signal processing. He is a Fellow of the IEEE.