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.