Oversampling and Coarse Quantization for Signals

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A Fast Reconstruction Method
for Bandlimited Functions from its Uniform Interlaced Samples

Dr. Jared Tanner

Statistics at Stanford University

Abstract:   For a number of applications it is either not possible or undesirable to acquire samples on a uniform mesh. An extension of Shannon's sampling theorem is presented in the case of uniform interleaved samples. From this extension we develop a fast O(N log N) algorithm in the case of a finite number of samples, N, are available. Moreover, by exploiting Gevrey regularity we are able to obtain precise root-exponential bounds on the convergence rate as the number of samples is increased.

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