Damped Sine Wave Parameter Extraction: Application to QCM-D Signals for Accurate Measurements

Quartz crystal microbalance with dissipation (QCM-D) monitoring is a sensing technique that finds diverse applications in chemical sensing, biosensing, and industrial fields. By monitoring the vibrational characteristics of a thin piezoelectric SiO2 resonator, this technique provides valuable information about the viscoelastic behavior of media in contact with its surface. This article evaluates the performance of algorithms applied to 10 MHz AT-cut QCM-D signals for estimating the frequency and time constant related to the fundamental resonant mode, extending the study to assess the effectiveness of disturbance rejection, particularly against quartz spurious oscillating modes. To this end, both damped single-tone and three-tone signals are analyzed to cover all potential outputs of a QCM-D in its fundamental bulk shear mode. Various estimation algorithms are considered: one operating in the frequency domain and others in the time domain, based on model fitting techniques with novel preprocessing steps for optimized initialization. The analysis utilizes signals from a QCM-D measurement set-up and signals simulated according to the characteristics of the AT-CUT crystals used. Among model fitting-based estimators, two techniques were developed for single-tone and three-tone signals, splitting the model-fitting problem into nonlinear and linear subproblems, demonstrating the best accuracy and processing time. The developed techniques meet strict measurement objectives, achieving frequency measurement resolution around 1 ppm (10 Hz) and decay time accuracy around 1 $\mu $ s, even with additive white Gaussian noise (AWGN) standard deviations of about 1% of the fundamental tone amplitude in water. These techniques are applicable in various contexts where recovering parameters from damped sine waves in the presence of white noise is required.