Phasing of harmonic components to optimize measured signal-to-noise ratios of transfer functions
John R. Lindsay Smith · Measurement Science and Technology · 1995
Much can be learnt about a system by studying how its various transfer functions vary with frequency. The best measured signal-to-noise ratio (SNR), and hence the most precise results, will occur when a sequence of stimuli, each containing only a single frequency, is applied to the system. However, it is often advantageous to shorten the total measurement time, with a consequent decrease in the measured SNR, by applying a stimulus that simultaneously contains several different frequency components. The author considers the various compromises between the measured SNR and the frequency components that are simultaneously present. The author concentrates upon improvements in the measured SNR that result from optimum phasing of the harmonic components. Calculations show that the SNR of a system with a transfer function that is substantially independent of frequency can thus be improved by a factor of approximately k0.4, where k denotes the number of frequencies that are simultaneously present. The measured SNR will thus vary approximately as k-0.6 if optimum waveforms are used.