A Statistical Analysis of Telephone Noise

Noise on telephone lines has puzzled and plagued people since the invention of the telephone. While it is common knowledge that telephone channel noise is nongaussian, nowhere in the literature is there a clear account of an adequate statistical characterization of telephone 1263 noise. In part, this is due to the fact that only recently have statistical tools been developed that are equal to the task. This paper attempts to adequately characterize some statistical properties of telephone channel noise by means of various nonparametric statistics and by mathematical models. It is encouraging to note that the results presented here do not contradict those found in earlier works. However, since only a small number of telephone line noise sample functions were examined, the results must be regarded as tentative, awaiting independent checks by other investigators. It is hoped the results presented here will stimulate communication theorists to investigate new methods for optimally processing signals corrupted by the nongaussian noise models presented here. Work along these lines might lead to optimum and practical suboptimum receiver structures for combating telephone noise. This in turn might permit greater insight into how noise limits telephone channel performance with regard to voice communication or data transmission. The authors have tried to keep the notation and nomenclature consistent with that used in statistics and probability theory. The reader is reminded, for example, that "empirical cumulative distribution function" refers to an estimate of the true "cumulative distribution function" based on observations of "empirical" data.