Foundations of Signal Processing

This comprehensive and accessible textbook introduces students to the basics of modern signal processing techniques.

Martin Vetterli (Author), Jelena Kova?evi? (Author), Vivek K Goyal (Author)

9781107038608, Cambridge University Press

Hardback, published 4 September 2014

738 pages, 200 b/w illus. 44 tables 190 exercises
25.2 x 18 x 3.5 cm, 1.61 kg

'Foundations of Signal Processing … is a pleasure to read. Drawing on the authors' rich experience of research and teaching of signal processing and signal representations, it provides an intellectually cohesive and modern view of the subject from the geometric point of view of vector spaces. Emphasizing Hilbert spaces, where fine technicalities can be relegated to backstage, this textbook strikes an excellent balance between intuition and mathematical rigor, that will appeal to both undergraduate and graduate engineering students. The last two chapters, on sampling and interpolation, and on localization and uncertainty, take full advantage of the machinery developed in the previous chapters to present these two very important topics of modern signal processing, that previously were only found in specialized monographs. The explanations of advanced topics are exceptionally lucid, exposing the reader to the ideas and thought processes behind the results and their derivation. Students will learn … why things work, at a deep level, which will equip them for independent further reading and research. I look forward to using this text in my own teaching.' Yoram Bresler, University of Illinois, Urbana-Champaign

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.

Subject Areas: Signal processing [UYS], Computer science [UY], Communications engineering / telecommunications [TJK], Electronics & communications engineering [TJ], Electrical engineering [THR], Numerical analysis [PBKS]