Hilbert Transforms: Volume 1

The definitive reference on Hilbert transforms covering the mathematical techniques for evaluating them, and their application.

Frederick W. King (Author)

9780521887625, Cambridge University Press

Hardback, published 27 April 2009

896 pages, 15 tables 350 exercises
24.2 x 16.2 x 5 cm, 1.52 kg

"The author gives detailed and exhaustive information on almost all properties of the Hilbert transform... the selected topics are presented in an easy-to-use style."
Lasha Ephremidze, Mathematical Reviews

The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications.

Preface
List of symbols
List of abbreviations
Volume I: 1. Introduction
2. Review of some background mathematics
3. Derivation of the Hilbert transform relations
4. Some basic properties of the Hilbert transform
5. Relationship between the Hilbert transform and some common transforms
6. The Hilbert transform of periodic functions
7. Inequalities for the Hilbert transform
8. Asymptotic behavior of the Hilbert transform
9. Hilbert transforms of some special functions
10. Hilbert transforms involving distributions
11. The finite Hilbert transform
12. Some singular integral equations
13. Discrete Hilbert transforms
14. Numerical evaluation of Hilbert transforms
References
Subject index
Author index.

Subject Areas: Signal processing [UYS], Mathematical modelling [PBWH], Calculus & mathematical analysis [PBK]