ABSTRACT
The primary interest in the study of analogue communications systems is the obscuring or masking of the transmitted signal by additive noise. This effect is most conveniently analysed by considering the spectral properties of the noise waveform. The situation in digital systems is quite different since only fixed signal levels are allowed. When these levels are obscured by additive noise the receiver is required to decide which of the allowed levels the noisy signal represents. If the receiver decides correctly the noise has no effect on the received signal whatever. If the receiver makes an incorrect decision the results can be catastrophic. Decision theory is based upon the statistical rather than the spectral properties of noise although, as one might expect, these properties are related. The most important statistical property of white noise, with respect to decision theory, is its amplitude distribution function.
