Estimating transfer functions of quadratically nonlinear systems

Sinusoidal and white noise input methods have previously been developed for estimating linear or higher order transfer functions of nonlinear systems. The authors describe a colored noise input method, which is based on partitioning the frequency band of interest into subbands, which results in less aliasing in the output and allows for greater precision in the transfer function estimates. With the scheme proposed the estimation of both the first and second order Volterra kernels can be improved. The Volterra kernels are assumed to be symmetric for simplicity. The focus is on a weakly nonlinear system, where the nonlinearity in the system is sufficiently small that a perturbation expansion may be truncated after the quadratic terms. At the expense of slightly more computations, the method provides considerably improved transfer function estimates