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Hilbert transforms

Author: Frederick W King
Publisher: Cambridge [England] ; New York : Cambridge University Press, 2009.
Series: Encyclopedia of mathematics and its applications, v. 124-125.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:

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

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Genre/Form: Electronic books
Additional Physical Format: Print version:
King, Frederick W., 1947-
Hilbert transforms.
Cambridge [Eng.] ; New York : Cambridge University Press, 2009-
(DLC) 2008013534
(OCoLC)214285969
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Frederick W King
ISBN: 9780511721458 0511721455 9780511735271 0511735278 9781107096080 1107096081
OCLC Number: 796857204
Description: 1 online resource (2 volumes (858, 660 pages)) : illustrations.
Contents: V. 1. Introduction --
Review of some background mathematics --
Derivation of the Hilbert transform relations --
Some basic properties of the Hilbert transform --
Relationship between the Hilbert transform and some common transforms --
The Hilbert transform of periodic functions --
Inequalities for the Hilbert transform --
Asymptotic behavior of the Hilbert transform --
Hilbert transforms of some special functions --
Hilbert transforms involving distributions --
The finite Hilbert transform --
Some singular integral equations --
Discrete Hilbert transforms --
Numerical evaluation of Hilbert transforms --
V. 2. Hilbert transforms in En --
Some further extensions of the classical Hilbert transform --
Linear systems and causality --
The Hilbert transform of waveforms and signal processing --
Kramers-Kronig relations --
Dispersion relations for some linear optical properties --
Dispersion relations for magneto-optical and natural optical activity --
Dispersion relations for nonlinear optical properties --
Some further applications of Hilbert transforms --
App. 1. Table of selected Hilbert transforms --
App. 2. Atlas of selected Hilbert transform pairs.
Series Title: Encyclopedia of mathematics and its applications, v. 124-125.
Responsibility: Frederick W. King.

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"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 Read more...

 
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