Nonlinearity Tests for Dynamic Processes

Coherence and apparent transfer function measurements for nonlinear physiological systems

Many studies of physiological systems utilize input-output experimental data to develop mathematical descriptions (models) of the system dynamics. Linear methods in the frequency domain are most commonly employed to obtain transfer function characteristics in the form of gain and phase plots. Coherence measurements are a companion tool in these studies, aimed at testing the linearity assumption and assessing the quality of the experimental data (i.e. the noise content). Many physiological systems possess intrinsic nonlinearities. The effect of these nonlinearities on the aforementioned measurements has been largely a matter of conjecture. This paper is a rigorous study of how coherence and apparent transfer function measurements are affected by system nonlinearities. The study is placed in the framework of the Volterra-Wiener theory of nonlinear systems, and it is intended to assist biomedical investigators in interpreting their experimental results in such cases. The class of quadratic nonlinear systems is discussed in greater detail, and simulation examples are presented in order to illustrate some of the more practically important analytical derivations.