Spectral shift of damped harmonic vibrations and methods for compensation

Resonators, especially quartz devices, can be used as remote sensors. The signal they produce as pulse response consists of a damped harmonic vibration where the natural frequency contains the information about the measured quantity. Under the viewpoint of noise and interference the most e$cient evaluation of the signal can be carried out in the frequency domain. For an undamped vibration the spectrum has a peak at the actual natural frequency. The problem is that the maximum of the spectrum of a damped vibration depends on uncertain parameters: damping and phase shift. In this paper several methods are discussed with which this e!ect can be eliminated, so that the natural frequency may be determined regardless of these parameters.