Dynamics of Correlated Random Pulse Trains

Based upon the concept of infinite impulse trains, the paper introduces a physically realizable stochastic model defined as an impulse process. This model allows the random amplitudes to be correlated. The input-output dynamics of linear filtering of the impulse process is investigated and the response spectral density, correlation and variance functions are derived and their behavior closely examined. Time series modelings by spectral and correlation approaches are described and digitally simulated samples for the impulse process and its response are presented. The analysis indicates that the impulse process and its filtered response process are very flexible and may be used to model a large class of random phenomena in engineering physics. The results of the analysis are also described with emphasis on their application in earthquake simulations.