Abstract:

ESDU 83041 gives a basic insight into and understanding of the concepts and definitions required to study random processes. No previous knowledge of statistics or harmonic analysis is assumed of the user, and the required mathematical analysis for the description of the statistical quantities is provided. After a summary of the concepts relating to random processes, the idea is introduced of an "ensemble" of individual "members" or records that, when treated as a whole, forms a random process. Ensemble averages are then used to quantify the properties of the random process and these are related to the statistical quantities such as probability distribution, probability density, correlation and spectral quantities involving Fourier series, integrals and transforms. The three classes of a random process (non-stationary, stationary and ergodic) are fully described; both the autocorrelation and the cross-correlation functions depend on the type of process and appropriate expressions are given for each class.