Filter bank realizations of Volterra kernels

A great many of processes in a nature are nonlinear, so their modeling requires an embedding of nonlinear parts into the model structure. One of the popular approaches to the nonlinear system modeling are Volterra series. Unfortunately, already the second order Volterra kernel requires high amount of coefficients for its identification and therefore a large number of computations for its realization. This paper shows several possibilities of reducing the amount of computations based on matrix decomposition of a second order Volterra kernel, and presents both mathematically accurate algorithms and approximate ones. Presented algorithms are in the form of filter bank structure. They can be used for highest order Volterra kernel realization as well.