A Theory and Method for Correlation Analysis of Nonstationary Signals

In this paper, a method is developed for obtaining cross-correlation functions and autocorrelation functions of signals which are generated by nonstationary processes. The theory of the method is based upon optimal approximation of the ensemble correlation function, when only one pair of signals is available for the correlation analysis. The use of the ensemble approximation approach allows the demonstration of the two uncertainties that always accompany correlation analysis of nonstationary signals. Moreover, this ensemble approximation approach makes possible the development of a mathematical synthesis procedure which specifies the optimal form of a realizable correlation analyzer for nonstationary signals. The synthesis procedure is described in detail for a specific but representative case and then is summarized for other cases. An experimental study has been performed which verifies the theory and demonstrates its effectiveness. The method is particularly suitable for analog and hybrid simulation.