Advanced Topics in Shannon Sampling and Interpolation Theory
Published on 7. January 2012
Book
Paperback/Softback
XIII, 360 pages
978-1-4613-9759-5 (ISBN)
Description
Advanced Topics in Shannon Sampling and Interpolation Theory
is the second volume of a textbook on signal analysis solely
devoted to the topic of sampling and restoration of
continuous time signals and images. Sampling and
reconstruction are fundamental problems in any field that
deals with real-time signals or images, including
communication engineering, image processing, seismology,
speech recognition, and digital signal processing. This
second volume includes contributions from leading
researchers in the field on such topics as Gabor's signal
expansion, sampling in optical image formation, linear
prediction theory, polar and spiral sampling theory,
interpolation from nonuniform samples, an extension of
Papoulis's generalized sampling expansion to higher
dimensions, and applications of sampling theory to optics
and to time-frequency representations. The exhaustive
bibliography on Shannon sampling theory will make this an
invaluable research tool as well as an excellent text for
students planning further research in the field.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1993
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XIII, 360 p.
Dimensions
Height: 244 mm
Width: 156 mm
Thickness: 21 mm
Weight
601 gr
ISBN-13
978-1-4613-9759-5 (9781461397595)
DOI
10.1007/978-1-4613-9757-1
Schweitzer Classification
Other editions
Additional editions
Robert J.II Marks
Advanced Topics in Shannon Sampling and Interpolation Theory
E-Book
12/2012
Springer
€53.49
Available for download
Robert J.II Marks
Advanced Topics in Shannon Sampling and Interpolation Theory
Book
12/1992
Springer
€85.55
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Content
1 Gabor's Signal Expansion and Its Relation to Sampling of the Sliding-Window Spectrum.- 1.1 Introduction.- 1.2 Sliding-Window Spectrum.- 1.3 Sampling Theorem for the Sliding-Window Spectrum.- 1.4 Examples of Window Functions.- 1.5 Gabor's Signal Expansion.- 1.6 Examples of Elementary Signals.- 1.7 Degrees of Freedom of a Signal.- 1.8 Optical Generation of Gabor's Expansion Coefficients for Rastered Signals.- 1.9 Conclusion.- 2 Sampling in Optics.- 2.1 Introduction.- 2.2 Historical Background.- 2.3 The von Laue Analysis.- 2.4 Degrees of Freedom of an Image.- 2.5 Superresolving Pupils.- 2.6 Fresnel SampHng.- 2.7 Exponential SampHng.- 2.8 Partially Coherent Fields.- 2.9 Optical Processing.- 2.10 Conclusion.- 3 A Multidimensional Extension of Papoulis' Generalized Sampling Expansion with the Application in Minimum Density Sampling.- I: A Multidimensional Extension of Papoulis' Generalized Sampling Expansion.- 3.1 Introduction.- 3.2 GSE Formulation.- 3.3 M-D Extension.- 3.4 Extension Generalization.- 3.5 Conclusion.- II: Sampling Multidimensional Band-Limited Functions At Minimum Densities.- 3.6 Sample Interdependency.- 3.7 Sampling Density Reduction Using M-D GSE.- 3.8 Computational Complexity of the Two Formulations.- 3.9 Sampling at the Minimum Density.- 3.10 Discussion.- 3.11 Conclusion.- 4 Nonuniform Sampling.- 4.1 Preliminary Discussions.- 4.2 General Nonuniform Sampling Theorems.- 4.3 Spectral Analysis of Nonuniform Samples and Signal Recovery.- 4.4 Discussion on Reconstruction Methods.- 5 Linear Prediction by Samples from the Past.- 5.1 Preliminaries.- 5.2 Prediction of Deterministic Signals.- 5.3 Prediction of Random Signals.- 6 Polar, Spiral, and Generalized Sampling and Interpolation.- 6.1 Introduction.- 6.2 Sampling in Polar Coordinates.- 6.3 SpiralSampling.- 6.4 Reconstruction from Non-Uniform Samples by Convex Projections.- 6.5 Experimental Results.- 6.6 Conclusions.- Appendix A.- Appendix B.- 7 Error Analysis in Application of Generalizations of the Sampling Theorem.- Foreword: Welcomed General Sources for the Sampling Theorems.- 7.1 Introduction - Sampling Theorems.- 7.2 Error Bounds of the Present Extension of the Sampling Theorem.- 7.3 Applications.- Appendix A.- A.1 Analysis of Gibbs' Phenomena.