Spectral analyses of non-linear interactions

Signals pertaining to motions of a non-linear oscillator and a set of quadratically coupled oscillators are studied using higher-order spectral analyses. The analyses are used to understand the role of phase coupling in non-linear interactions betwen two or more Fourier components. For certain motions of weakly non-linear systems, analytical approximations are obtained for the relevant higher-order spectra and coherence functions. The analytical approximations are useful in understanding the dependence of bispectra on the non-linearities. Numerical studies are conducted to verify analytical predictions and to illustrate the usefulness of spectral analyses for different cases. (C) 1996 Academic Press Limited