The zero crossing problem
Anthony Sofo, Arthur Taber Jones · Victoria University Research Repository (Victoria University) · 1993
We analyze a second order nonlinear differential equation that is useful in the zero crossing problem.We show that our calculated values are in agreement with the simulated values in the region of time 't, 0.1 < 't < 0.9. Intro du ctj onConsider a sample function of a random process as shown.Researchers have been particularly interested in the statistics of the points where the sample function crosses the zero-axis, and in the probability density function of the intervals between these crossings.Kac [1] in 1943 initiated some of the early investigations into this area, and more recently by Barnett [2].Wong [3] has obtained some results based on approximate techniques.The zero-crossing problem is a long standing one and it concerns the problem of determining the relevant statistics of the zero-crossings of random communication signals.This problem has relevance not only in communication theory, but also in the study of ocean waves, random vibrations, earthquakes, speech recognition, signal processing and frequency measurements.Seumahu (4], through the application of the z-transformation has been able to derive a second order non-linear differential equation in the z-domain.Gopalsamy and Lalli [5] have also investigated zero crossings in integrodifferential equations.