Hilbert space methods in signal processing /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Kennedy, Rodney A. (Engineer) (Autor), Sadeghi, Parastoo (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2013.
Temas:
Signal processing > Mathematics.
Hilbert space.
Traitement du signal > Mathématiques.
Espace de Hilbert.
COMPUTERS > Information Theory.
TECHNOLOGY & ENGINEERING > Signals & Signal Processing.
Hilbert space
Signal processing > Mathematics
Acceso en línea:Texto completo

MARC

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100 1 |a Kennedy, Rodney A.  |c (Engineer),  |e author. 
245 1 0 |a Hilbert space methods in signal processing /  |c Rodney A. Kennedy, Australian National University, Canberra, Parastoo Sadeghi, Australian National University, Canberra. 
260 |a Cambridge :  |b Cambridge University Press,  |c 2013. 
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504 |a Includes bibliographical references (pages 395-401) and index. 
588 0 |a Print version record. 
505 0 |6 880-01  |a 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. 
520 |a 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. 
546 |a English. 
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650 0 |a Signal processing  |x Mathematics. 
650 0 |a Hilbert space. 
650 6 |a Traitement du signal  |x Mathématiques. 
650 6 |a Espace de Hilbert. 
650 7 |a COMPUTERS  |x Information Theory.  |2 bisacsh 
650 7 |a TECHNOLOGY & ENGINEERING  |x Signals & Signal Processing.  |2 bisacsh 
650 7 |a Hilbert space  |2 fast 
650 7 |a Signal processing  |x Mathematics  |2 fast 
700 1 |a Sadeghi, Parastoo,  |e author. 
776 0 8 |i Print version:  |a Kennedy, Rodney A. (Engineer).  |t Hilbert space methods in signal processing.  |d Cambridge : Cambridge University Press, 2013  |z 9781107010031  |w (OCoLC)841251265 
856 4 0 |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=539272  |z Texto completo 
880 0 |6 505-00/(S  |a Contents -- Preface -- Part I Hilbert Spaces -- 1 Introduction -- 1.1 Introduction to Hilbert spaces -- 1.1.1 The basic idea -- 1.1.2 Application domains -- 1.1.3 Broadbrush structure -- 1.1.4 Historical comments -- 1.2 Infinite dimensions -- 1.2.1 Why understand and study infinity-- 1.2.2 Primer in transfinite cardinals -- 1.2.3 Uncountably infinite sets -- 1.2.4 Continuumas a power set -- 1.2.5 Countable sets and integration -- 2 Spaces -- 2.1 Space hierarchy: algebraic, metric, geometric -- 2.2 Complex vector space -- 2.3 Normed spaces and Banach spaces -- 2.3.1 Norm and normed space -- 2.3.2 Convergence concepts in normed spaces -- 2.3.3 Denseness and separability -- 2.3.4 Completeness of the real numbers -- 2.3.5 Completeness in normed spaces -- 2.3.6 Completion of spaces -- 2.3.7 Complete normed spaces-Banach spaces -- 2.4 Inner product spaces and Hilbert spaces -- 2.4.1 Inner product -- 2.4.2 Inner product spaces -- 2.4.3 When is a normed space an inner product space-- 2.4.4 Orthonormal sets and sequences -- 2.4.5 The space l2 -- 2.4.6 The space L2(Ω) -- 2.4.7 Inner product and orthogonality with weighting in L2(Ω) -- 2.4.8 Complete inner product spaces-Hilbert spaces -- 2.5 Orthonormal polynomials and functions -- 2.5.1 Legendre polynomials -- 2.5.2 Hermite polynomials -- 2.5.3 Complex exponential functions -- 2.5.4 Associated Legendre functions -- 2.6 Subspaces -- 2.6.1 Preamble -- 2.6.2 Subsets, manifolds and subspaces -- 2.6.3 Vector sums, orthogonal subspaces and projections -- 2.6.4 Projection -- 2.6.5 Completeness of subspace sequences -- 2.7 Complete orthonormal sequences -- 2.7.1 Definitions -- 2.7.2 Fourier coefficients and Bessel's inequality -- 2.8 On convergence -- 2.8.1 Strong convergence -- 2.8.2 Weak convergence -- 2.8.3 Pointwise convergence -- 2.8.4 Uniform convergence -- 2.9 Examples of complete orthonormal sequences. 
880 8 |6 505-01/(S  |a 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. 
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