Direct synthesis signal sets for multi-input system identification

Abstract The design of correlated direct synthesis signal sets for the identification of multi-input systems is considered. These signals possess favorable characteristics for identification tests. Firstly, they do not contain power at harmonic multiples of two and three; this allows the reduction of the effects of nonlinear distortion on the linear estimate. Secondly, the signals are ternary which simplifies physical implementation. Existing results on the properties of individual direct synthesis signals are extended to the investigation of pairs of signals. The peak crosscorrelations are derived and it is shown that they depend on the generating signal class. The theoretical results provide a basis for the selection of signal sets with small peak crosscorrelations; this improves the estimation accuracy in identification tests. An important advantage of the proposed design over the conventional design using uncorrelated signal sets is the greater uniformity in the estimation accuracy of the different channels in the multi-input system. This is achieved by having all the signals in a set sharing the same power spectrum.