Wavelet correlations of nonstationary signals

Two approaches to the analysis of nonstationary random signals are proposed and studied. The first approach is based on the adaptive Morlet wavelet that allows variations in time and frequency resolution of signals using an auxiliary control parameter. The second approach is related to the application of double correlation function that represents correlation of continuous wavelet transforms of two signals calculated in time and frequency domains. The advantages of the proposed correlation function in comparison with alternative correlation functions, in particular, analysis of both time and frequency correlations of nonstationary signals are outlined. Applications of the proposed approaches in the analysis of various transient processes in physics are discussed.