A Statistical Analysis of Telephone Noise

The results of a statistical analysis of telephone noise are presented. The analysis consists of two stages: an exploratory data analysis stage, where the data are characterized through various nonparametric statistics and a model-building stage, where the data are matched to models. The exploratory data analysis stage involved examination of noise waveforms, power spectra, and covariance estimates. The results show that telephone noise consists of a deterministic component (sinusoids at various frequencies) and a stochastic component. It is assumed that these components add. The data are filtered to remove the deterministic component. Next, central moment estimates are presented, as well as first-order amplitude statistics (histograms and empirical cumulative distributions) for these filtered data. The results indicate that the filtered data appear wide-sense stationary over short periods of time (typically 1 second) and, although close to gaussian, are distinctly nongaussian. The model-building stage involved fitting the filtered data to two classes of models. The first class of models is based on symmetric stable distributions that arise from the central limit theorem. The second class of models assumes two different physical processes that contribute to the random component of telephone noise: The low-variance process is assumed to be gaussian, while the high-variance component is assumed to be a filtered Poisson process. Both classes of models agree intuitively with the physical processes generating telephone noise and are mathematically tractable. Based largely on graphical tests, both models appear to fit the filtered data reasonably well.