In radar and communication, signal reception is made difficult by randomly fluctuating waveforms that modulate or add to the desired signal. These waveforms, which change unpredictably as a function of time, are conveniently described statistically. They are observables of physical processes that are apparently controlled by a random mechanism; such functions of time are called random processes. There are many random processes in nature, such as the voltage generated across a resistor by thermally excited electrons, the spatial position of a particle undergoing Brownian motion, atmospheric pressure fluctuations, and so on. The mathematical representation of random processes introduced in this chapter is one of the tools required in the remainder of this book. Those wishing a broader and deeper understanding of this subject may consult the bibliography at the end of the chapter.

Chapter Contents:

• 4.1 Introduction
• 4.2 Characterization of a Random Process
• 4.3 Statistically Independent Random Processes
• 4.4 Stationary and Ergodicity
• 4.5 Power Spectral Density
• 4.6 Wiener-Khnintchine Theorem
• 4.7 Shape of Power Spectral Density
• 4.8 The Gaussian Random Process
• 4.9 Fourier Series Representation of a Gaussian Random Process
• 4.10 (Karhunen-Loéve) Orthonormal Expansion of a Gaussian Random Process
• 4.11 The Narrowband Gaussian Random Process
• Problems
• Recommended Bibliography

Inspec keywords: random processes; radar detection

Other keywords: randomly-fluctuating waveforms; random mechanism; particle spatial position; signal reception; thermally-excited electrons; random process; physical process; Brownian motion; atmospheric pressure fluctuations

Subjects: Radar theory; Signal detection; Other topics in statistics