Pseudorandom signals to estimate apparent transfer and coherence functions of nonlinear systems: applications to respiratory mechanics

For pseudorandom (PRN) input stimuli, general expressions are derived for the apparent transfer (Z) and coherence ( gamma ²) functions of nonlinear systems that can be represented by a Volterra series. To avoid the problems that are shown here to be associated with harmonic distortions and to minimize the influence of crosstalk, a family of pseudorandom signals which are especially suited for the estimation of Z and gamma ² in mechanical measurement of physiological systems at low frequencies is proposed. The components in the signals cannot be reproduced as linear combinations of two or more frequency components of the input. In a second-order system, this completely eliminates the bias, while in higher order but not strongly nonlinear systems, the interactions among the components are reduced to such a level that the response can be considered as if it were measured with independent sine waves of an equivalent amplitude. It is also shown that the values of gamma ² are not appropriate for assessing linearity of the system. The theory is supported by simulation results and experimental examples.