Signal-Detection Studies, with Applications

The word detection suggests a decision between just two alternatives: either a signal was transmitted, or it was not. Typically, however, such decisions are made repeatedly at short intervals of time, with the effect that a multiplicity of possibilities are involved, namely the time intervals in which signals are received, and perhaps also the carrier frequencies at which they are transmitted. In radar and sonar systems, rotating directional receivers map one, two, or three dimensions of space upon the time axis, so that the observation of time is translatable into an observation of position. In these applications, of course, the received signal is a reflection of one transmitted by the observer, and the aircraft or other object to be detected is not attempting to communicate with the ob403 404 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1 9 5 5 server. Telegraphy and PCM are applications in which the signals do represent attempts to communicate. In all cases, random noise is present, and will hide signals whose intensity is sufficiently low. If the bandwidth of the noise accompanying the signal is considerably larger than that of the signal, the best practical procedure is well known to be to pass the signal-plus-noise through a bandpass filter whose bandwidth approximates the larger of the following: (a) The bandwidth of the signal, (b) The reciprocal of the time available for detecting the signal.1 If the frequency of the signal is not known in advance, one of course moves the pass-band of the filter up and down the frequency scale and thus searches for the signal in frequency as well as in time; the present discussion applies equally well to this case.