Abstract
Abstract
When a periodic multi-harmonic signal is contaminated by a random noise, the identification of harmonic amplitudes can be performed from the autocorrelation function. However, the latter is not indicative of harmonic phases. Both the amplitudes and the phases can be determined by a time-synchronous averaging procedure, but this requires an accurate knowledge of the multi-harmonic component period obtained from a separate measurement that is not always readily available. Hence, there has been previous research to avoid the necessity of measuring the period and it is the approach followed by this paper. The methodology used is based on the fact that the presence of a periodic component makes the probability density function of the composite signal non-Gaussian. By equalizing the theoretical high-order moments of the composite signal to the corresponding moments calculated for the measured data record, a closed-form solution is derived for the amplitudes and the phases of the bi-harmonic component.