Design of multilevel perturbation signals with harmonic properties suitable for nonlinear system identification

A method is described for determining the levels of multilevel pseudorandom perturbation signals generated from maximum-length sequences in Galois fields that give the signals the desirable characteristics that their even harmonics are suppressed and their odd harmonics are uniform. The method uses the fact that a short sequence comprised of the signal levels converted from the nonzero field elements taken in a particular order must have corresponding characteristics. Analytical expressions are obtained for the signal level conversions that are necessary for the signal to possess these characteristics. The results are tabulated in symbolic form for 3-level, 5-level and 7-level signals generated in the fields GF(3), GF(5), GF(7), GF(9), GF(11) and GF(13). The method is then extended to signals in which harmonic multiples of 2 and 3 are suppressed and nonzero harmonics are uniform, and similar results are tabulated for GF(7) and GF(13). An example is used to illustrate the application of the results.