A Random Nonstationary Pulse Train Model

Abstract

A simple and mathematically tractable model of a nonstationary process is developed. The process is the sum of waves where the parameters of the waves are random. Explicit expressions for the mean and autocorrelation function at each position as a function of time are obtained. In the case of infinite time, the model evolves into a stationary process. The time-frequency distribution at each position is also obtained. An explicit example is given where the initial waves are Gaussian. The case where there is dispersion in the propagation is also discussed.

Keywords

nonstationary process / mean and autocorrelation function / time-frequency distribution / Gaussian waves