Advances in Shannon’s Sampling Theory
Allan G. Piersol · Shock and Vibration · 1994
To most shock and vibration engineers, the sampling theorem, usually credited to C.E. Shannon, is that theorem that states the following: if an analog signal is band-limited to a frequency range from 0 to W Hz, then it is completely determined by a series of discrete values spaced IJ,.W seconds apart.It is the basic theorem that dictates the sampling rate needed to accurately convert a measured shock or vibration signal to discrete values for digital data analysis purposes.This book by Zayed shows the implications of sampling theory go far beyond the above simple interpretation and application.Specifically, one of the objectives ofthe book stated in the Preface is "To provide a moderately concise survey of the present state of knowledge ofthe subject and to shed some light on the new connections between sampling theory and other branches of mathematical analysis, such as the theory of boundary-value problems, the theory of frames and wavelets and multiresolution analysis of Hilbert spaces."The author achieves this objective very effectively.The first chapter provides an excellent historic review of the subject, and makes an effort to relate the mathematical terminology used throughout the book to terms more familiar to communication engineers.The second chapter summarizes sampling theory for band-limited signals, including a brief discussion of oversampling.The third chapter presents a series of 28 theorems that provide the foundation for most sampling theory applications.Of particular practical interest in this chapter are the discussions and theorems related to non-uniform sampling, and the various errors associated with sampling, i.e., truncation, aliasing, amplitude, and time-jitter errors.The remaining seven chapters pursue the previously stated objective of the book, and are probably of interest only to applied mathemati-Shock and Vibration, VoU, No.4, p.