Abstract :
An analysis is made, and numerical results are tabulated, of the processes of addition and multiplication of signals (comprising tone or noise) in the presence of random-noise backgrounds. These processes may be carried out on the input signals, in which case coincidence in time and phase of the signals is required, or on the signals after they have been rectified and smoothed (i.e. on the envelopes), in which case coincidence is required only in time. If the backgrounds are uncorrelated with one another, then the addition or multiplication of two or more scans together results in an increase in detectability of the signal. It is shown that, in general, multiplication is not more advantageous than addition from the point of view of signal/noise ratios, and as it is more difficult to perform in practice, it cannot be universally recommended. But it is undoubtedly better than addition in certain cases, notably those in which long-term stability of adjustment is required and constant or predictable phase relationships permit multiplication of the inputs before rectification. Some subjective evidence is brought forward and discussed in relation to the difficult question of whether the better signal/noise performance given by a quadratic response as compared with a linear response is really indicative of a higher probability of detection. The conclusions are not clear, but it is possible that this is the case.
