Sung-Rung Huang

On estimating the amplitude of harmonic vibration from the Doppler spectrum of reflected signals

The Doppler spectrum of echoes from a sinusoidally vibrating scatterer has discrete spectral lines weighted by Bessel functions of the first kind. Because the signal and spectrum are complicated functions of the vibration amplitude, a number of different approaches have been tried in the past to estimate the vibration amplitude, given a received signal. Here, a new and simple relationship between the spread (or variance) of the Doppler spectrum and the vibration amplitude is derived. A method of estimating the vibration amplitude is proposed based on this relation and a noise compensation procedure is also demonstrated. The performance of the estimators is studied through simulations. High accuracy is predicted under proper sampling conditions even when the signal‐to‐noise ratio is poor. Slight deviations from single‐frequency oscillation, as would be caused by nonlinear or nonideal medium or source effects, are found to have little contribution to the total estimation error.

Time domain Doppler estimators of the amplitude of vibrating targets

Five basic algorithms using time domain techniques are described in this paper to estimate the amplitude and frequency of relatively low‐frequency vibration of a target that is interrogated with a relatively high‐frequency wave. The estimations are based on the Doppler shift generated by the vibrating target, which produces a frequency modulated echo. All algorithms presented here use only a small fraction of the low‐frequency vibration cycle to obtain the estimated parameters; therefore, real‐time imaging of vibration can be made in many applications. The described algorithms complement each other to cover a wide range of the estimated parameters and different sampling, scanning, and imaging criteria. Simulations show that these time domain algorithms have good noise performance and low sensitivity to nonlinearities of the vibration that may be present in nonideal conditions.