Advances in Shannon’s Sampling Theory

Abstract

1. Introduction and a Historical Overview -- 2. Shannon Sampling Theorem and Band-Limited Signals -- 3. Generalizations of Shannon Sampling Theorems -- 4. Sampling Theorems Associated With Sturmliouville Boundary-Value Problems -- 5. Sampling Theorems Associated With Self-Adjoint Boundary-Value Problems -- 6. Sampling by Using Green's Function -- 7. Sampling Theorems and Special Functions -- 8. Kramer's Sampling Theorem and Lagrange-Type Interpolation in N Dimensions -- 9. Sampling Theorems for Mulidimensional Signals -- The Feichtinger-Grochenig Sampling Theory -- 10. Frames and Wavelets: A New Perspective on Sampung Theorems.