An algorithm for accurately estimating the harmonic magnitudes and phase shifts of periodic signals with asynchronous sampling

A digital sampling algorithm that uses two high-resolution integrating voltmeters in a master-slave configuration for accurately measuring the harmonic magnitudes and phase angles of two low-noise, low-frequency, arbitrary voltage signals is presented. It is shown that it is possible to measure up to 64 harmonic magnitudes of 60-Hz signals with an uncertainty of less than 13 μV/V relative to the fundamental using commercial stable signal generators and high-resolution digital voltmeters. It is also possible to measure the phase shift between the fundamental components of two equally-synthesized 60-Hz signals with about 3.8% total harmonic distortion with an uncertainty of less than 2.5 μrad. Even lower uncertainties can be obtained for low-distortion signals. The algorithm was applied to the measurement of the harmonics of periodic arbitrary signals generated by a commercial source. The differences between computed and measured values of harmonic magnitude suggest that stable digitally-synthesized signal generators can be used as calculable standards of harmonic distortion with an accuracy of less than 6 parts in 10⁵ relative to the fundamental.