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C h a p t e r
RANDOM PROCESSES
AND SPECTRAL ANALYSIS
CHAPTER OBJECTIVES
• Random processes
• Power spectral density
• Characteristics of linear systems
• Gaussian random processes
• Matched filters
The mathematics used to describe random signals and noise will be examined in this
chapter. Recall from Chapter 1 that random, or stochastic, signals (in contrast to deterministic
signals) are used to convey information. Noise is also described in terms of statistics.
Thus, knowledge of random signals and noise is fundamental to an understanding of
communication systems.
This chapter is written with the assumption that the reader has a basic understanding of
probability, random variables, and ensemble averages, all of which are developed in
Appendix B. If the reader is not familiar with these ideas, Appendix B should be studied now
just like a regular chapter. For the reader who has had courses in this area, Appendix B can be
used as a quick review.
Random processes are extensions of the concepts associated with random variables
when the time parameter is brought into the problem. As we will see, this enables frequency
response to be incorporated into the statistical description.
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