论文标题
离散阻尼正弦振荡的快速参数测定
Rapid parameter determination of discrete damped sinusoidal oscillations
论文作者
论文摘要
我们提出了不同的计算方法，以快速提取离散采样的阻尼正弦信号的信号参数。我们根据估计此类信号的频率所需的准确性，精度和计算时间来比较基于时间和频率域的计算方法，并观察到精度和速度之间的一般权衡。我们的动机是对阻尼正弦信号的精确而快速的分析，因为这些信号鉴于最近在腔体增强的极化仪和椭圆测量中的实验发展相关，因此相关的时间尺度和频率通常在$ \ sim1-10 \，μ$ s和$ $ $ s和$ \ sim1-100 $ mhz ranges上，这通常在$ \ sim1-10 \，sim1-10 \中。在这样的实验工作中，在开发研究动力学效果和/或开发便携式仪器时，具有高精度和精度的单发分析变得很重要。我们的结果表明，在线，运行时尚，微秒解决的分析分析是可能的，分数不确定性以$ 10^{ - 6} $的水平为$ 10^{ - 6} $，并且使用原始实验证明的证明是可能的，我们表明，使用基于频率的分析方法，我们可以在KHZ速率和准确的信号中监视和分析信号，并在Microseccect中降低信号。
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 $\sim1-10\,μ$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.
