Numerical Bayesian Methods Applied to Signal Processing

This book is concerned with the processing of signals that have been sam- pled and digitized. The fundamental theory behind Digital Signal Process- ing has been in existence for decades and has extensive applications to the fields of speech and data communications, biomedical engineering, acous- tics, sonar, radar, seismology, oil exploration, instrumentation and audio signal processing to name but a few [87]. The term "Digital Signal Processing", in its broadest sense, could apply to any operation carried out on a finite set of measurements for whatever purpose. A book on signal processing would usually contain detailed de- scriptions of the standard mathematical machinery often used to describe signals. It would also motivate an approach to real world problems based on concepts and results developed in linear systems theory, that make use of some rather interesting properties of the time and frequency domain representations of signals. While this book assumes some familiarity with traditional methods the emphasis is altogether quite different. The aim is to describe general methods for carrying out optimal signal processing.