Wavelets
A Student Guide

Makes the intrinsically advanced theory of wavelets accessible to senior undergraduate students with a mathematical background.

Peter Nickolas (Author)

9781107612518, Cambridge University Press

Paperback / softback, published 11 January 2017

274 pages, 20 b/w illus. 230 exercises
22.8 x 15.1 x 1.5 cm, 0.41 kg

'What is really nice with this book is its style, which leads the student step by step through different ideas, theorems and proofs. It explains the reason behind new concepts, discusses their shortcomings, and uses these as a motivation to introduce other concepts.' Salim Salem, MAA Reviews

This text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.

Preface
1. An overview
2. Vector spaces
3. Inner product spaces
4. Hilbert spaces
5. The Haar wavelet
6. Wavelets in general
7. The Daubechies wavelets
8. Wavelets in the Fourier domain
Appendix: notes on sources
References
Index.

Subject Areas: Calculus & mathematical analysis [PBK], Algebra [PBF], Mathematics [PB]