Accurate Power Spectrum Estimation of a Damped Sinusoidal Signal in Low SNR Cases Based on a Newly Defined Transfer Function

This paper is concerned with a method to estimate the power spectrum of a periodic damped sinusoidal signal contaminated by high-level noise components when there are fluctuations in the period. A correlation between two spectral components exists at and around the resonant frequency of a damped sinusoidal signal. By using this property, the authors introduce a new transfer function defined from the resonant frequency component to every other component around the resonant frequency to estimate the power spectrum of the damped sinusoidal signal. Since it can be assumed that there is no correlation between these two different frequencies for the noise components, the noise components in the cross spectrum at the two different frequencies decrease with the averaging operation. Consequently, the power spectrum of the damped sinusoidal signal is accurately estimated from the observed signals, even if the signal-to-noise ratio (SNR) is very low. The proposed method developed here is satisfactorily confirmed by simulation experiments. This method is further applied to the estimation of the power spectra of the vibration signals radiated from normal and defective automobile engines.