The measurement of the kernels of the Volterra series model of a nonlinear system is generally carried out as follows; first a parametric model is derived by applying orthogonal expansions to the kernels, and then the parameters are optimally determined in the sense of the least mean square error of the input/output experiments of the system.
In this method, if the input is a white Gaussian signal, the amount of computation required is greatly reduced whenever an arbitrary set of orthonormal functions is used for the expansion of the kernels. On the other hand, if the input is a stationary nonwhite Gaussian signal, the set of orthonormal functions cannot be taken arbitrarily for the purpose of computational reduction.
In this paper, the method of measuring the kernels, where an arbitrary set of orthonormal functions can be taken without the assumption that the input is white, is presented by applying Karhunen-Loeve expansion theorem. The key of the present method is that a nonstationary Gaussian random process is generated from an arbitrary set of orthonormal functions used for the expansion of the kernels and a set of uncorrelated Gaussian random variables, and it is used as the input.