A DIGITAL TECHNIQUE TO ESTIMATE 2ND-ORDER DISTORTION USING HIGHER-ORDER COHERENCE SPECTRA

A digital spectral method to evaluate second-order distortion of a nonlinear system, which can be represented by Volterra kernels up to second order and which is subjected to a random noise input, is discussed. The importance of departures from the commonly assumed Gaussian excitation is investigated. The Hinich test, which makes use of the statistical properties of bispectrum, is shown to be an appropriate test for orthogonality in the system identification of a second-order Volterra system. Tests for Gaussianity of two important sources, which are commonly used for Gaussian inputs in nonlinear system identification are presented: 1) commercial software routines for simulation experiments and 2) noise generators for practical experiments. The deleterious effects and misleading results of assuming a Gaussian input when, in fact, it is not, are demonstrated. The random input method to evaluate (in terms of the second-order Volterra kernels and distortion factors) the second-order distortion of a nonlinear system is compared with the sine-wave input method using both simulation and experimental data. The proposed approach is utilized to model, identify, and quantify the linear response and second-order distortion products of a loudspeaker in the low frequency band by using higher order coherence spectra.