A Mathematical Model

Abstract

The mathematical model presented in this chapter is intended to be sufficiently general to include the examples of Chapter 1 as well as many others, and yet sufficiently specific to enable us to apply the concepts of statistical-decision theory as well. We shall examine the general reception problem as a statistical-decision problem and hence shall assume certain statistics of the messages and channel disturbances depending on the criterion for system evaluation prescribed and the set of decisions permitted by the receiver. We shall also have to make certain assumptions concerning the nature of the available data, such as whether it resulted from discrete or continuous sampling of the observed waveform. Finally, we must specify the performance criterion by which we are seeking the optimal system.