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This comprehensive and accessible textbook introduces students to the basics of modern signal processing techniques.
List of contents
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.
About the author
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.
Summary
This comprehensive, accessible textbook covers the basics of signal processing, building up from fundamental principles to practical applications. It uses engineering notation to make mathematical concepts easy to follow, includes numerous homework problems and is accompanied by an extensive Mathematica® companion and instructor solutions manual.
Report
'This is a major book about a serious subject - the combination of engineering and mathematics that goes into modern signal processing: discrete time, continuous time, sampling, filtering, and compression. The theory is beautiful and the applications are so important and widespread.' Gil Strang, Massachusetts Institute of Technology
