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BestsellerE-book
Author Kennedy, Rodney A. (Engineer), author.

Title Hilbert space methods in signal processing / Rodney A. Kennedy, Australian National University, Canberra, Parastoo Sadeghi, Australian National University, Canberra.

Publication Info. Cambridge : Cambridge University Press, 2013.

Item Status

Description 1 online resource (xvii, 420 pages) : illustrations
Physical Medium polychrome
Description text file
Bibliography Includes bibliographical references (pages 395-401) and index.
Contents 1. Introduction -- 2. Spaces -- 3. Introduction to operators -- 4. Bounded operators -- 5. Compact operators -- 6 Integral operators and their kernels -- 7. Signals and systems on 2-sphere -- 8. Advanced topics on 2-sphere -- 9. Convolution on 2-sphere -- 10. Reproducing kernel Hilbert spaces -- Answers to problems.
8.9 Azimuthally symmetric concentrated signals in polar cap -- 8.10 Uncertainty principle for azimuthally symmetric functions -- 8.11 Comparison with time-frequency concentration problem -- 8.12 Franks generalized variational framework on 2-sphere -- 8.12.1 Variational problemformulation -- 8.12.2 Stationary points of Lagrange functional G(f) -- 8.12.3 Elaborating on the solution -- 8.13 Spatio-spectral analysis on 2-sphere -- 8.13.1 Introduction and motivation -- 8.13.2 Procedure and SLSHT definition -- 8.13.3 SLSHT expansion -- 8.13.4 SLSHT distribution and matrix representation -- 8.13.5 Signal inversion -- 8.14 Optimal spatio-spectral concentration of window function -- 8.14.1 SLSHT onMars topographic data -- 9 Convolution on 2-sphere -- 9.1 Introduction -- 9.2 Convolution on real line revisited -- 9.3 Spherical convolution of type 1 -- 9.3.1 Type 1 convolution operator matrix and kernel -- 9.4 Spherical convolution of type 2 -- 9.4.1 Characterization of type 2 convolution -- 9.4.2 Equivalence between type 1 and 2 convolutions -- 9.5 Spherical convolution of type 3 -- 9.5.1 Alternative characterization of type 3 convolution -- 9.6 Commutative anisotropic convolution -- 9.6.1 Requirements for convolution on 2-sphere -- 9.6.2 A starting point -- 9.6.3 Establishing commutativity -- 9.6.4 Graphical depiction -- 9.6.5 Spectral analysis -- 9.6.6 Operator matrix elements -- 9.6.7 Special case -- one function is azimuthally symmetric -- 9.7 Alt-azimuth anisotropic convolution on 2-sphere -- 9.7.1 Background -- 10 Reproducing kernel Hilbert spaces -- 10.1 Background to RKHS -- 10.1.1 Functions as sticky-note labels -- 10.1.2 What is wrong with L2(Ω)-- 10.2 Constructing Hilbert spaces from continuous functions -- 10.2.1 Completing continuous functions -- 10.3 Fourier weighted Hilbert spaces -- 10.3.1 Pass the scalpel, nurse.
Summary This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Signal processing -- Mathematics.
Signal processing -- Mathematics.
Hilbert space.
Hilbert space.
Genre/Form Electronic books.
Electronic book.
Added Author Sadeghi, Parastoo, author.
Other Form: Print version: Kennedy, Rodney A. (Engineer). Hilbert space methods in signal processing. Cambridge : Cambridge University Press, 2013 9781107010031 (OCoLC)841251265
ISBN 9780511844515 (electronic book)
0511844514 (electronic book)
9781107336452 (electronic book)
1107336457 (electronic book)
9781299773059 (MyiLibrary)
1299773052 (MyiLibrary)
9781107333130 (e-book)
110733313X (e-book)
9781107334793
1107334799
9781107010031
1107010039