Abstract :
The factors which determine the possibility of observing a pulse signal in the presence of noise are discussed. The theoretical and practical results quoted in the existing literature are surveyed, and some alternative proofs are offered which, though less rigorous than the classical treatment, have a more intuitive physical foundation. The analysis recalls the familiar principle of matching the I.F. response of the receiver to the frequency content of the pulse, in the presence of ?white? noise. A comparison is made with the best smoothing network for reproducing a continuous signal in the presence of noise. The effect of the detector law is shown to be negligible provided it gives a monotonic increase of output with increase of input; the law affects the mapping of the distribution in the output, but the relative probabilities that a particular amplitude arises from noise and signal, or from noise alone, are unchanged. The behaviour of any rectifier in the region where signal and noise are of comparable magnitude leads to loss of performance if the overall filtration is incorrectly distributed between the IF. and V.F. stages. The mean power required to detect each pulse separately is comparable with the noise power in a band equal to the repetition frequency: the additional information capacity is taken up in defining the phase of the pulse within the interval. A succession of pulses can be combined by superposition and the ratio of signal to noise power is improved in the ratio of the number of pulses combined: if the signal at the detector is already at the threshold of noise the incoming signal power can only be lowered by the square root of this number making the mean input power necessary comparable with the noise power in a band whose reciprocal is the geometric mean of the repetition period and the observation period. This feature of detector operation could only be overcome by superposition before detection, which is usually impracticable. The paper also i- ncludes a short discussion of ways in which practical requirements can modify the abstract conclusions.
