Titlebook: Sampling: Theory and Applications; A Centennial Celebra Stephen D. Casey,Kasso A. Okoudjou,Brian M. Sadler Book 2020 This is a U.S. governm

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Prolate Shift Frames and Sampling of Bandlimited Functions,erating sinc function is poorly localized in time. This work reviews and extends some recent related work of the authors regarding frames for the Paley–Wiener space generated by shifts of prolate spheroidal wave functions, and the question of tradeoff between localization of the generators and of the dual frames is considered.

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Reconstruction of Signals: Uniqueness and Stable Sampling, problems ask for which sets of frequencies . is the exponential system . ., or constitutes a . in the space .. on a given set . of finite measure? When . is a single interval, these problems were essentially solved by A. Beurling, A. Beurling and P. Malliavin in terms of appropriate densities of th

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Sampling Theory in a Fourier Algebra Setting,ct is not as well-known as it might be, possibly because the approximate sampling theorem, central to our discussion, had what could be called a mysterious birth and a confused adolescence. We also discuss functions of the familiar bandlimited and bandpass types, showing that they too have a place i

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Sampling Series, Refinable Sampling Kernels, and Frequency Band Limited Functions,sion, particular attention is paid to sampling series whose kernels are refinable..After developing the basic properties of the sampling kernels under study, we consider three families of such kernels: (1) damped cardinal sines, (2) the fundamental functions for cardinal spline interpolation, and (3

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Prolate Shift Frames and Sampling of Bandlimited Functions,expressed as a superposition of shifts of finitely many bandlimited generators. The coefficients of these expansions can be regarded as generalized samples taken at a Nyquist rate determined by the number of generators and basic shift rate parameter. When the shifts of the generators form a frame fo

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