Introduction to Shannon Sampling and Interpolation Theory

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Robert J. Marks II

   Pages 1-6

3. Fundamentals of Fourier Analysis and Stochastic Processes

   • Robert J. Marks II

   Pages 7-32

4. The Cardinal Series

   • Robert J. Marks II

   Pages 33-56

5. Generalizations of the Sampling Theorem

   • Robert J. Marks II

   Pages 57-110

6. Sources of Error

   • Robert J. Marks II

   Pages 111-166

7. The Sampling Theorem in Higher Dimensions

   • Robert J. Marks II

   Pages 167-224

8. Continuous Sampling

   • Robert J. Marks II

   Pages 225-278

9. Back Matter

   Pages 279-324

   PDF

Much of that which is ordinal is modeled as analog. Most computational engines on the other hand are dig- ital. Transforming from analog to digital is straightforward: we simply sample. Regaining the original signal from these samples or assessing the information lost in the sampling process are the fundamental questions addressed by sampling and interpolation theory. This book deals with understanding, generalizing, and extending the cardinal series of Shannon sampling theory. The fundamental form of this series states, remarkably, that a bandlimited signal is uniquely specified by its sufficiently close equally spaced samples. The contents of this book evolved from a set of lecture notes prepared for a graduate survey course on Shannon sampling and interpolation theory. The course was taught at the Department of Electrical Engineering at the University of Washington, Seattle. Each of the seven chapters in this book includes a list of references specific to that chapter. A sequel to this book will contain an extensive bibliography on the subject. The author has also opted to include solutions to selected exercises in the Appendix.

• analog
• electrical engineering
• signal

• Interactive Systems Design Laboratory, Department of Electrical Engineering, University of Washington, Seattle, USA

  Robert J. Marks

Policies and ethics