A Signal Theoretic Introduction to Random Processes

6PROTOTYPICAL RANDOM PROCESSES

6.1 INTRODUCTION

In this chapter, the prototypical, and important, random processes encountered in the physical sciences are defined. The Bernoulli, generalized Bernoulli, the random walk, Poisson, the random telegraph signal, shot noise, clustered, signalling, jitter, white noise, 1/f noise, birth–death, and orthogonal increment random processes are defined. The experiments, and notation for random processes, defined in the previous chapter are used. The simple as possible random process is the Bernoulli random process.

6.2 BERNOULLI RANDOM PROCESSES

Definition: Bernoulli Random Processes

A Bernoulli random process is defined on a Bernoulli experiment according to

(6.1)

Clearly,

(6.2)

One example of a Bernoulli random process is defined by the signal sample space

(6.3)

This random process, and the defined signals, is illustrated in Figure 6.1.

Figure 6.1 Two signals arising from the Bernoulli random process defined in the text.

6.2.1 Generalized Bernoulli Random Processes

Definition: Generalized Bernoulli Random Process

A generalized ...