Random Sampling Using Shannon Interpolation and Poisson Summation Formulae

Details Random Sampling Using Shannon Interpolation and Poisson Summation Formulae Random Sampling Using Shannon Interpolation and Poisson Summation Formulae

2009-09-14

arxiv.org/abs/0909.2292v3

Computer Science

Information Theory

This is a preprint version of research report, which may submit to some conference or journal

Scientific paper

This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast and efficient observation matrix filling technique was implemented by the classic Shannon interpolation and Poisson summation formulae. The numerical results for the trigonometric signal, the Gaussian-modulated sinusoidal pulse, and the square wave were demonstrated and discussed. The work may give some help for future work in theoretical study and practical implementation of the random sampling.

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