A Generalized Sampling Theorem for Frequency Localized Signals
Abstract
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obtained (though the former might be "practically perfect" in many cases). For an arbitrary finite-energy signal the frequency localization is performed by a prefilter realizing a crosscorrelation with a function of prescribed properties. The range of the filter, the so-called localization space, is described in some detail. Regular sampling is applied and a reconstruction formula is given. For the reconstruction error a general error estimate is derived and connections between a critical sampling interval and notions of "soft bandwidth" for the prefilter are indicated. Examples based on the sinc-function, Gaussian functions and B-splines are discussed.
Cite
@article{arxiv.0707.0285,
title = {A Generalized Sampling Theorem for Frequency Localized Signals},
author = {Edwin Hammerich},
journal= {arXiv preprint arXiv:0707.0285},
year = {2009}
}
Comments
20 pages, extended version of talk at International Workshop on Sampling Theory and Applications SampTA07, Thessaloniki, Greece, June 1-5, 2007. Submitted to Sampl. Theory Signal Image Process