Introduction to Random Signals and Noise

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Introduction

1.1 RANDOM SIGNALS AND NOISE

In (electrical) engineering one often encounters signals that do not have a precise mathematical description, since they develop as random functions of time. Sometimes this random development is caused by a single random variable, but often it is a consequence of many random variables. In other cases the causes of randomness are not clear and a description is not possible, but the signal is characterized by means of measurements only.

A random time function may be a desired signal, such as an audio or video signal, or it may be an unwanted signal that is unintentionally added to a desired (information) signal and disturbs the desired signal. We call the desired signal a random signal and the unwanted signal noise. However, the latter often does not behave like noise in the classical sense, but it is more like interference. Then it is an information bearing signal as well, but undesired. A desired signal and noise (or interference) can, in general, not be distinguished completely; by means of well-defined signal processing in a receiver, the desired signal may be favoured in a maximal way whereas the disturbance is suppressed as much as possible. In all cases a description of the signals is required in order to be able to analyse its impact on the performance of the system under consideration. Especially in communication theory this situation often occurs. The random character as a function of time makes the signals difficult to describe ...