ABSTRACT
The use of the Volterra series in dynamics stems from a seminal paper, in which the series was applied to nonlinear differential equations for the first time. One can think of the series as a generalization of the Taylor series from functions to functionals. The higher-order frequency response functions or Volterra kernel transforms are provided as the multi-dimensional Fourier transforms of the kernels. The fundamental problem associated with the Volterra series is the determination of either the kernels or the kernel transforms. This must be done analytically if the equations of motion are known or numerically if time series are given for the input and output processes. This chapter presents a technique which allows the Hilbert transform distortion to be derived term by term from a Volterra series expansion of the system frequency response function. The single-input–single-output Volterra series is established as a powerful tool in nonlinear system theory.
