On the Use of Gram-Charlier Series to Represent Noise

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Abstract
The stochastic time series produced by the arrival at random times of identical individual events is considered. It is shown that if the shape of the individual events and of the resulting autocorrelation function and power spectrum are each represented by a Gram-Charlier series, relatively simple relationships exist between the different sequences of coefficients. These relationships are most serviceable when the coefficients of the autocorrelation function are used as the primary quantities. If the band width of the noise is ``moderate,'' the series has a small number of terms and consequently is practical from a computational viewpoint. The formulas are applied to the experimental data of noise produced when current is forced backwards through a silicon crystal. The shape of the individual noise events is determined from a knowledge of the experimental autocorrelation function. As a check on the analysis the power spectrum and the expected number of zeros per second are computed from the Gram-Charlier series and compared with the experimental data.

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