Irregular Sampling

Abstract

Abstract A sampling process employing sample points that are not equidistantly spaced is usually called irregular, or sometimes non-uniform. Irregular sampling arises mathematically by simply asking the question “What is special about equidistantly spaced sample points?”; and then finding, as we shall in this chapter, that the answer is “Within certain limitations, nothing at all”.In practice it is often said that irregular sampling is the norm rather than the exception. For example, sample points are likely to be disturbed by “noise”, meaning any random influences beyond our control. Again, it might he convenient to reconstruct a function from the locations of its zeros, or places where it crosses some datum function. Such points are, of course, intrinsic to the object function.Again, sample points might be required to have a deterministic distribution, and then we ask if all functions of a given class can be reconstructed from their samples at these points. This is the only kind of irregular sampling we shall discuss here. A review of the applied aspects of irregular sampling can be found in Marvasti (1993), and there are many interesting studies on this theme in the Conference Proceedings of the 1995 workshop on sampling theory and applications, Jurmala, Latvia, 1995, published by the Institute of Electronics and Computer Science, Riga, Latvia.