AN EXTENSION OF NYQUISTS THEOREM TO NONUNIFORMLY SAMPLED FINITE-LENGTH DATA

This paper examines non-uniformly sampled functions on a finite interv al. The aim is to investigate what conditions must be satisfied in ord er to recover the baseband spectrum from such data. It is shown that t he concept of band limitation inherent in Nyquist's theorem must be ge neralized into a quantity termed primary interval bandwidth limitation . This property is explored and various algorithms are developed, incl uding an extension of the classical band-limited interpolation formula . Measures are obtained that provide guidelines for assessing where ap proximate techniques can be employed and the use of these in adaptive scenarios is considered. The key results are illustrated by a set of n umerical examples. The findings are presented in the context of time v ariables, but the approach is applicable to any type of sample domain. The treatment is one-dimensional, as are the examples discussed, but the extension to multiple dimensions is immediate and straightforward.