Optimum Resolution Bandwidth for Spectral Analysis of Stationary Random Vibration Data

This article presents a methodology for selecting the frequency resolution bandwidth for the spectral analysis of stationary random vibration signals in an optimum manner. Specifically, the resolution bandwidth that will produce power spectral density estimates with a minimum mean square error is determined for any given measurement duration (averaging time), and methods of approximating the optimum bandwidth using practical spectral analysis procedures are detailed. The determination of the optimum resolution bandwidth requires an estimate for the damping ratio of the vibrating structure that produced the measured vibration signal and the analysis averaging time. It is shown that the optimum resolution bandwidth varies approximately with the 0.8 power of the damping ratio and the bandwidth center frequency, and the −0.2 power of the averaging time. Also, any resolution bandwidth within ±50% of the optimum bandwidth will produce power spectral density (PSD) estimates with an error that is no more than 25% above the minimum achievable error. If a damping ratio of about 5% for structural resonances is assumed, a constant percentage resolution bandwidth of 1/12 octave, but no less than 2.5 Hz, will provide a near optimum PSD analysis for an averaging time of 2 seconds over the frequency range from 20 to 2000 Hz. A simple scaling formula allows the determination of appropriate bandwidths for other damping ratios and averaging times.