Combined crosscorrelation method for the measurement of 2nd-order Volterra kernels

Abstract

A method is proposed for combining the estimates of the values of the 2nd-order Volterra kernel of a nonlinear system, obtained by crosscorrelation experiments using pseudorandom ternary input signals, so that the effects of some of the undesirable nonzero values of the 4th-order autocorrelation functions of the signals are cancelled. Relationships between pairs of pseudorandom ternary signals, and their 4th-order autocorrelation functions which make them suitable for this purpose, are established, and their performance in this application is investigated. The performance with this combined-crosscorrelation method is shown to be generally superior to that with the direct-crosscorrelation method, within common limits imposed by the intrusion of nonzero diagonal values. The characteristic polynomials and performance indices of pseudorandom ternary signals with superior performance are tabulated, and an example is used to illustrate the solution of a typical problem.