Design of nonbinary signals with low peak factors

Limitations associated with the determination of frequency response characteristics using the fast Fourier transform and pseudo-random binary signals (PRBS) when testing practical systems are noted. They arise from the fundamental nature of the real work in that physical systems have some degree of nonlinear behaviour. Consequently, when using composite frequency signals to obtain a linear estimate of a system, harmonics are generated by each frequency component of the signal and also by intermodulation and they result in pronounced scatter in the spectral estimates. The author has previously shown (1977, 1978) that a test signal consisting of an assemblage of discrete sinusoids of frequencies which are odd and prime number multiples of some fundamental, which is itself excluded from the signal, provides excellent harmonic rejection capability compared with PRBS and inverse repeat PRBS. This signal is called the prime sinusoid signal. the resulting amplitude probability distribution however, means that the dynamic range of the signal makes it in many cases unacceptable when testing engineering systems. The paper concerns the design of suitable multifrequency signals for test purposes, and in particular the evaluation and extension of various synthesising procedures to obtain a low peak factor when using the prime sinusoid signal. To provide a benchmark for comparison, a composite signal made of consecutive harmonics is also considered