We study sampling theory because of its intrinsic mathematical interest and because of its importance for applications in the sciences and engineering. One feature stands out in both these activities as being of prime importtance: for members of certain function classes there is an equivalence between the function(a continuous information source) on the one hand, and a suitable collection of its samples (a discrete information source) on the other.
One of the chief ways of effecting this equivalence mathematically is to expand the function into a series containing the samples. The main purpose of this book is to provide a broad-based introduction to the mathematical study of sampling series.
1. An introduction to sampling theory
2. Background in Fourier analysis
3. Hilbert spaces, bases and frames
4. Finite sampling
5. From finite to infinite sampling series
6. Sampling for Bernstein and Paley--Wiener spaces
7. More about Paley-- Wiener spaces
8. Kramer's Lemma
9. Contour integral methods
10. Irregular sampling
,etc.