Adaptive Filtering

4	Discrete-Time Random Processes

4.1    DISCRETE RANDOM SIGNALS, PROBABILITY DISTRIBUTIONS, AND AVERAGES OF RANDOM VARIABLES

Most signals in practice are not deterministic but random. However, they can be described by precise mathematical analysis whose tools are contained in the theory statistical analysis. In this chapter, we are dealing only with discrete random signals. This can always be accomplished by sampling the continuous signals at sampling rates at least twice their highest frequency, thus avoiding aliasing. Remember that the signals we receive are band limited because all signals must be detected by a physical (not ideal) transducer, such as a voltmeter or a receiver, which measures the electrocardiogram, the movement during ...