An extension of Nyquist's theorem to non-uniformly sampled finite length data
✍ Scribed by M. R. Belmont
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 923 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0890-6327
No coin nor oath required. For personal study only.
✦ Synopsis
This paper examines non-uniformly sampled functions on a finite interval. The aim is to investigate what conditions must be satisfied in order to recover the baseband spectrum from such data. It is shown that the concept of band limitation inherent in Nyquist's theorem must be generalized into a quantity termed primary interval bandwidth limitation. This property is explored and various algorithms are developed, including an extension of the classical band-limited interpolation formula. Measures are obtained that provide guidelines for assessing where approximate techniques can be employed and the use of these in adaptive scenarios is considered. The key results are illustrated by a set of numerical examples. The findings are presented in the context of time variables, 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.