Applications of Frequency and Wavenumber Nonlinear Digital Signal Processing to Nonlinear Hydrodynamics Research

Volterra series representations of weakly nonlinear systems have been utilized in studies of both nonlinear hydrodynamics and nonlinear system identification. In the Volterra approach, the linear and nonlinear features of the system are described by the so-called linear, quadratic, cubic, etc., Volterra kernels. In the time domain these kernels correspond to the linear, quadratic, cubic, etc., impulse responses of the system, whereas, in the frequency domain they correspond to the linear, quadratic, cubic, etc., transfer functions. Of particular practical importance is the fact that the linear and nonlinear physics of the physical system is imbedded in the kernels, thus their experimental determination is often of the utmost importance in nonlinear hydrodynamics in particular, and nonlinear system identification, in general.