Identifying System Non-Linearities by Fusing Signal Bispectral Signatures

Abstract

Higher-order statistics investigate the phase relationships between frequency components, an aspect which cannot be treated using conventional spectral measures such as the power spectrum. Among the widely used higher-order statistics, the bispectrum ranks prominently. By delving into higher-order correlations, the bispectrum offers a means of extracting additional merits and insights from frequency coupling, enhancing our understanding of complex signal interactions. This analytical approach overcomes the limitations of traditional methods, providing a more comprehensive view of the complex relationships within the frequency domain. In this paper, the extensive use of the bispectrum in various scientific and technical areas is firstly emphasized by presenting very recent applications. The main scope of this work is to investigate the consequences of various non-linearities in the creation of phase couplings. Specifically, the quadratic, the cubic and the logarithmic non-linearities are examined. In addition, simple recommendations are given on how the underlying nonlinearity could be detected. The total approach is novel, considering the capability to distinguish from the bispectral content if two non-linearities are simultaneously present.