Introduction

In this introductory chapter, we begin by reviewing the long history of coherence in the physical and engineering sciences. The idea of coherence in physics relates to interference, diffraction, and propagation phenomena in which waves can maintain constructive or destructive phase alignment. The Van Cittert-Zernike theorem, the Hanbury Brown-Twiss effect, and, more recently, the detection of cosmic gravitational waves at the Laser Interferometer Gravitational-Wave Observatory (LIGO) are illustrative examples of the use of coherence in classical and modern physics. In electrical engineering, coherence appears in phenomena of diffraction of an electromagnetic wave passing through a slit, when analyzing the intensity of the electric field radiated by an antenna in a given direction, or in the study of correlators, matched filters, and ambiguity functions in radar and sonar. This chapter also serves to justify the use of complex signals, which will be extensive throughout the book, as well as to present the problem of extracting information from a multi-sensor array of series analysis that motivates our interest in coherence.