Zeros of Gaussian Noise
Gerald M. White · Journal of Applied Physics · 1958
For many years statisticians and research workers in communication theory have been interested in the problem of the ``zeros'' i.e., the statistics of the times a random function crosses through its average value. At present very few of the desired results are amenable to analytic or numerical solution; therefore, an experiment was designed for generating and measuring the zeros of Gaussian noise having various spectral shapes. This article contains several experimentally determined distributions and statistics. Those that could be checked with numerical calculations {e.g., P[+z(t)|+z(0)], the probability of finding a zero in an increment of time Δt, t seconds after a zero has occurred} agreed closely with their calculated values. The others, e.g., W(N,T), the number of zeros in an increment of time T, verified what would be intuitively expected. The article also briefly outlines the equipment used in this investigation.