Design of Pseudorandom Signals for Linear System Identification

The design of pseudorandom signals which have fixed autocorrelation functions, and therefore fixed spectra, dependent only on the class and period of the signal is described. The theory behind the generation of several classes of pseudorandom signals is discussed, and their properties are explained. These include maximum length binary signals based on shift register sequences, as well as several other classes of binary and near-binary signals, namely, the quadratic residue binary and ternary, Hall binary and twin prime binary signals. The maximum length design extends to the multilevel case, where the sequence-to-signal conversion determines not only the harmonic properties but the period of the resulting signal. An interesting class of truncated signals arises from certain well-defined choices. The design of direct synthesis ternary signals and the suboptimal direct synthesis ternary signals is discussed. Finally, an application example is presented for linear identification of a system in the presence of nonlinear distortion.