9780198534969

Sampling Theory in Fourier and Signal Analysis Volume 2: Advanced Topics

by ;
  • ISBN13:

    9780198534969

  • ISBN10:

    0198534965

  • Format: Hardcover
  • Copyright: 2000-02-24
  • Publisher: Oxford University Press

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Summary

Volume 1 in this series laid the mathematical foundations of samplingtheory; Volume 2 surveys the many applications of the theory both withinmathematics and in other areas of science. Topics range over a wide variety ofareas, and each application is given a modern treatment.

Table of Contents

List of contributors
xiv
Applications of sampling theory to combinatorial analysis, stirling numbers, special functions and the Riemann zeta function
1(37)
P. L. Butzer
M. Hauss
Introduction
1(2)
Binomial coefficient function
3(7)
Gauss summation formula
10(2)
Stirling functions
12(4)
Stirling functions and the Riemann zeta function ζ(s)
16(4)
Euler formulae for ζ(s) and summation formulae involving the Hilbert transform
20(12)
Sampling expansions of particular special functions
32(6)
Sampling theory and the arithmetic Fourier transform
38(18)
W. J. Walker
Historical development
38(4)
The AFT algorithm
42(3)
Aliasing properties of the DFT and AFT
45(5)
The summability algorithm
50(2)
Deletion properties of the AFT algorithm
52(2)
Deletion properties of the summability algorithm
54(2)
Derivative sampling---a paradigm example of multichannel methods
56(22)
J. R. Higgins
Introduction
56(1)
A brief survey of derivative sampling
57(3)
The Riesz basis method in its multichannel setting
60(6)
Applications to constructive function theory
66(8)
Multidimensional derivative sampling
74(4)
Computational methods in linear prediction for band-limited signals based on past samples
78(18)
D. H. Mugler
Introduction
78(1)
Asymptotic expansions
79(2)
An optimal set of prediction coefficients
81(2)
An integral equation
83(2)
Size of the optimal prediction coefficients
85(1)
Alternative computational methods
86(2)
Suppressing the effects of noise on the prediction
88(4)
Non-uniformly spaced samples
92(2)
Conclusion
94(2)
Interpolation and sampling theories and linear ordinary boundary value problems
96(34)
W.N. Everitt
G. Nasri-Roudsari
Introduction
96(10)
Second-order problems
106(14)
Shannon-type interpolation formulae
120(7)
Higher-order problems
127(3)
Sampling by generalized kernels
130(28)
R.L. Stens
Introduction
130(2)
Notation and preliminary results
132(4)
Approximation of non-band-limited functions
136(13)
Approximation of band-limited functions
149(9)
Sampling theory and wavelets
158(29)
A. Fischer
Introduction
158(4)
The continous wavelet transform
162(6)
Interpolation on shift-invariant spaces
168(5)
Multiresolution analysis
173(4)
Sampling approximation
177(10)
Approximation by translates of a radial function
187(22)
N. Dyn
Introduction
187(4)
Quasi-interpolation on regular grids
191(7)
Optimal approximation schemes on regular grids
198(3)
Approximation on quasi-uniformly scattered centres
201(8)
Almost sure sampling restoration of band-limited stochastic signals
209(24)
T. Pogany
Historical overview and oversampling
209(5)
The Piranashvili-Lee theory
214(5)
The Gaposhkin-Klesov theory
219(3)
Irregular-derivative Kotel' nikov series
222(3)
Derivative sampling and the Gaposhkin theory
225(6)
Gaposhkin theory and irregular sampling
231(2)
Abstract harmonic analysis and the sampling theorem
233(33)
M. M. Dodson
M. G. Beaty
Introduction
233(1)
Locally compact abelian groups
234(8)
Fourier theory
242(7)
An abstract sampling theorem
249(9)
Some applications
258(8)
References 266(23)
Author index 289(4)
Subject index 293

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