Effects of nonlinearities on the measurement of weighting functions by crosscorrelation using pseudorandom signals

In this paper, expressions are obtained for the errors introduced into the estimate of a system weighting function obtained by crosscorrelation when nonlinearities that may be described by a Volterra functional series are present. Explicit results are given for systems with second-and third-order nonlinearities, tested by pseudorandom signals derived from binary and ternary m sequences. It is shown that the principal errors are of two distinct types: a systematic error that is the same for all pseudorandom signals of a common type, and an unsystematic error that depends on relationships between members of the m sequence from which the pseudorandom signal is derived. The unsystematic error may be removed from a range of interest extending over the settling time of the system by an appropriate choice of test signal, and those pseudorandom signals most suitable for this purpose are identified. An example is used both to illustrate and to validate the results obtained.