Local sampling set conditions in weighted shift-invariant signal spaces

Abstract

How to represent a continuous signal in terms of a discrete sequence is a fundamental problem in sampling theory. Most of the known results concern global sampling in shift-invariant signal spaces. But in fact, the local reconstruction from local samples is one of the most desirable properties for many applications in signal processing, e.g. for implementing real-time reconstruction numerically. However, the local reconstruction problem has not been given much attention. In this article, we find conditions on a finite sampling set X such that at least in principle a continuous signal on a finite interval is uniquely and stably determined by their sampling value on the finite sampling set X in shift-invariant signal spaces.

Keywords:

• local sampling
• sampling set
• shift-invariant space

AMS Subject Classifications::

• 94A20
• 42C15
• 15A09

Acknowledgements

This project is partially supported by the National Natural Science Foundation of China (10801136, 10871213), the Natural Science Foundation of Guangdong Province (07300434), the Fundamental Research Funds for the Central Universities (10lgpy27) and the Scientific Research Fund of Hunan Provincial Education Department (No. 10B040).