Rapid parameter determination of discrete damped sinusoidal oscillations

TL;DR

This paper compares computational methods for rapid, precise analysis of discretely sampled damped sinusoidal signals, demonstrating their application in high-speed polarimetry and ellipsometry measurements with microsecond resolution.

Contribution

It introduces and evaluates different computational approaches for fast and accurate parameter extraction of damped sinusoidal signals in the context of recent experimental techniques.

Findings

Frequency-based analysis achieves high precision at microsecond time scales.

Online analysis can monitor signals at kHz rates with microsecond resolution.

Fractional uncertainties can reach levels of 10^{-6} in practical measurements.

Abstract

We present different computational approaches for the rapid extraction of the signal parameters of discretely sampled damped sinusoidal signals. We compare time- and frequency-domain-based computational approaches in terms of their accuracy and precision and computational time required in estimating the frequencies of such signals, and observe a general trade-off between precision and speed. Our motivation is precise and rapid analysis of damped sinusoidal signals as these become relevant in view of the recent experimental developments in cavity-enhanced polarimetry and ellipsometry, where the relevant time scales and frequencies are typically within the $\sim1-10\,\mu$s and $\sim1-100$MHz ranges, respectively. In such experimental efforts, single-shot analysis with high accuracy and precision becomes important when developing experiments that study dynamical effects and/or when developing portable instrumentations. Our results suggest that online, running-fashion, microsecond-resolved analysis of polarimetric/ellipsometric measurements with fractional uncertainties at the $10^{-6}$ levels, is possible, and using a proof-of-principle experimental demonstration we show that using a frequency-based analysis approach we can monitor and analyze signals at kHz rates and accurately detect signal changes at microsecond time-scales.