ABSTRACT
Up to now, we have reviewed the basic knowledge on the theory of probability, which is the fundamental tool for the study of random processes. In addition, we have learned the approach of using two-dimensional (2D) deterministic probability distribution functions to handle one-dimensional (1D) random events. We also introduced random processes in Chapter 3, the time domain approach, where the nature of such a dynamic process was unveiled. From the viewpoint of probability distributions, a random process can have many, if not infinite, pieces of random distributions, instead of a single one as a set of random variables does. Although it is not necessary, in most cases, we will use time as new indices to describe and handle these multiple distribution functions and refer to the methodology as a three-dimensional (3D) approach. Furthermore, in Chapter 4, the functions in the time domain, either the time-varying process itself, which is random, or the correlation functions, which become deterministic through the operation of mathematical expectation, were transferred into the frequency domain. Although it is still a “3D” approach, the corresponding Fourier transforms provided spectral analysis. The latter is a powerful tool to describe the frequency components of a random process.
