Significance testing for wavelet bicoherence and its application in analyzing nonlinearity in turbulent shear flows
Zhongfu Ge · Physical Review E · 2010
Wavelet-based bispectral analysis has been applied in various physical and engineering fields in recent years, but discussion of its significance testing, which distinguishes statistically meaningful results from those due to random noise, has been scarce and incomplete in the literature. Previously derived significance levels for wavelet bicoherence were either preliminary or based on numerical simulations of a limited sample size. The present study reviewed relevant previous works analytically identified the sampling distribution of the estimated wavelet bicoherence and derived expressions for its significance levels for any given probability value. Its application in analyzing a turbulent shear flow around a bluff body was demonstrated in detail. The significance testing developed here helped to identify significant quadratic couplings among a triad of scales in a separated turbulent shear layer over very short time intervals. The results obtained here can be applied to a wide variety of research topics for detecting nonlinearity in physical systems.