Measurement of second-order Volterra kernels using pseudorandom ternary signals

Abstract

The problem of measuring the second-order Volterra kernel of a non-linear system by cross-correlation using a pseudo-random ternary test signal is considered. It is shown that the kernel values may be determined by a shift-and-add procedure, applied to the diagonal measurements obtained by removing a bias from the cross-correlation function of the system output and the square of the system input. The complete information content of experimental results may be extracted by this procedure, but it is shown to be preferable to extract only uniformly distributed kernel values, and the pseudo-random ternary signals which yield the greatest number of such values are tabulated. Implementation is shown to be simpler than conventional methods, and amenable to the application of discrete Fourier transforms. An example is used to illustrate the method.