Bispectral analysis: comparison of two windowing functions

Abstract

Amongst all the normalized forms of bispectrum, the bicoherence is shown to be a very useful diagnostic tool in experimental studies of nonlinear wave interactions in plasma, as it measures the fraction of wave power due to the quadratic wave coupling in a self-excited fluctuation spectrum [1, 2]. In order to avoid spectral leakage, the application of a windowing function is needed during the bicoherence computation. Spectral leakage from statistically dependent components are of crucial importance in the discrimination between coupled and uncoupled modes, as they will introduce in the bicoherence spectrum phase-coupled modes which in reality do not exist. Therefore, the windowing function plays a key role in the bicoherence estimation. In this paper, two windowing methods are compared: the multiplication of the initial signal by the Hanning function and the subtraction of the straight line which links the two extremities of the signal. The influence of these two windowing methods on both the power spectrum and the bicoherence spectrum is showed. Although both methods give precise results, the Hanning function appears to be the more suitable window.