PHASING OF HARMONIC COMPONENTS TO OPTIMIZE MEASURED SIGNAL-TO-NOISE RATIOS OF TRANSFER-FUNCTIONS

Much can be learnt about a system by studying how its various transfer functions vary with frequency. The best measured signal-to-noise rati o (SNR), and hence the most precise results, will occur when a sequenc e of stimuli, each containing only a single frequency, is applied to t he system. However, it is often advantageous to shorten the total meas urement time, with a consequent decrease in the measured SNR, by apply ing a stimulus that simultaneously contains several different frequenc y components. This paper considers the various compromises between the measured SNR and the frequency components that are simultaneously pre sent. It concentrates upon improvements in the measured SNR that resul t from optimum phasing of the harmonic components. Calculations show t hat the SNR of a system with a transfer function that is substantially independent of frequency can thus be improved by a factor of approxim ately k(0.4), where k denotes the number of frequencies that are simul taneously present. The measured SNR will thus vary approximately as k- (0.6) if optimum waveforms are used.