Fluctuation analysis of nonideal shot noise: Application to the NeuromuscularJunction

Abstract

Procedures are described for analyzing shot noise and determining the waveform, w(t), mean amplitude, (h), and mean rate of occurrence, (r), of the shots under a variety of nonideal conditions that include: (a) slow, spurious changes in the mean, (b) nonstationary shot rates, (c) nonuniform distribution of shot amplitudes, and (d) nonlinear summation of the shots. The procedures are based upon Rice’s (1944. Bell Telephone Systemjournal. 23: 282- 332) extension of Campbell’s theorem to the second (variance), λ2, third (skew), λ3, and fourth, λ4, semi-invariants (cumulants) of the noise. It is shown that the spectra of λ2 and λ3 of nonstationary shot noise contain a set of components that are proportional to (r) and arise from w(t), and a set of components that are independent of (r) and arise from the temporal variations in r(t). Since the latter components are additive and are limited by the bandwidth of r(t), they can be removed by appropriate filters; then (r) and (h) can be determined from the λ2 and λ3 of the filtered noise. We also show that a factor related to the ratio (λ3)2/(λ2)(λ4) monitors the spread in the distribution ofshot amplitudes and can be used to correct the estimates of (r) and (h) for the effects of that spread, if the shape of the distribution is known and if r(t) is stationary. The accuracy of the measurements of λ4 is assessed and corrections for the effects of nonlinear summation of A2, λ3, and λ4 are derived. The procedures give valid results when they are used to analyze shot noise produced by the (linear) summation of simulated miniature endplate potentials, which are generated either at nonstationary rates or with a distribution of amplitudes. © 1986, Rockefeller University Press., All rights reserved.