With much material not previously found in book form, this book fills a gap by discussing the equivalence of signal functions with their sets of values taken at discreet points comprehensively and on a firm mathematical ground. The wide variety of topics begins with an introduction to the main ideas and background material on Fourier analysis and Hilbert spaces and their bases. Other chapters discuss sampling of Bernstein and Paley-Wiener spaces; Kramer's Lemma and its application to eigenvalue problems; contour integral methods including a proof of the equivalence of the sampling theory; the Poisson summation formula and Cauchy's integral formula; optimal regular, irregular, multi-channel, multi-band and multi-dimensional sampling; and Campbell's generalized sampling theorem. Mathematicians, physicists, and communications engineers will welcome the scope of information found here.
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This book is an excellent introduction into various aspects of sampling theory, written by a long-standing expert in this field. The book covers most of the standard topics in sampling theory....The book is aimed towards a mathematical audience and may form the basis for a one semester graduate corse. But it is also highly recommended for those of the scientific community, who wish to inform themselves about the basics of the theory, particularly those in mathematics, applied mathematics, and engineering.
About the Author
John Rowland Higgins is at Anglia Polytechnic University.
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Let us suppose that a function f is defined for every point of some domain D, and has a series representation there of the form in which {n} is a collection of points of D, and {Sn} is some set of suitable expansion functions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
aliasing error bound, cardinal series, stable sampling, many real zeros, minimal sampling rate, sampling series, general sampling theorem, prolate spheroidal wave functions, summation formulae, integral analogue, convergence principle, irregular sampling, unconditional bases, reproducing kernel, reconstruction function, fundamental region, sampling theory, exponential type, real signal, delta method Key Phrases - Capitalized Phrases (CAPs): (learn more)
Kramer's Lemma, New York, Academic Press, Proof First, Signal Proc, Cambridge University Press, Conference Proceedings, Hausdorff Young, Analysis Optim, Hadamard's Factorization Theorem, N-dimensional Lebesgue New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let us suppose that a function f is defined for every point of some domain D, and has a series representation there of the form in which {n} is a collection of points of D, and {Sn} is some set of suitable expansion functions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
aliasing error bound, cardinal series, stable sampling, many real zeros, minimal sampling rate, sampling series, general sampling theorem, prolate spheroidal wave functions, summation formulae, integral analogue, convergence principle, irregular sampling, unconditional bases, reproducing kernel, reconstruction function, fundamental region, sampling theory, exponential type, real signal, delta method Key Phrases - Capitalized Phrases (CAPs): (learn more)
Kramer's Lemma, New York, Academic Press, Proof First, Signal Proc, Cambridge University Press, Conference Proceedings, Hausdorff Young, Analysis Optim, Hadamard's Factorization Theorem, N-dimensional Lebesgue New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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