论文标题
抛物线差异PVAR对权力法的非整体指数的响应和不确定性
Response and Uncertainty of the Parabolic Variance PVAR to Non-Integer Exponents of the Power Law
论文作者
论文摘要
振荡器的波动描述为相位或频率噪声谱，或者根据小波方差作为测量时间的函数。频谱通常通过“功率定律”近似，即带有频率整数指数的劳伦（Laurent）多项式。本文扩展了PVAR应用的域，PVAR是一个小波方差，它在相位数据上使用线性回归来估计频率，并称为“抛物线”，因为这种回归等于应用于频率波动的抛物线形重量函数。反过来，PVAR是相关的，因为它可以改善广泛修改的Allan方差（MVAR），从而在较短的测量时间内可以在相同的置信度下检测相同的噪声过程。更具体地说，我们提供（i）PVAR对频率的一般情况下PVAR对频率频谱的响应的分析表达，以及（ii）统计不确定性的有用的近似表达。
Oscillator fluctuations are described as the phase or frequency noise spectrum, or in terms of a wavelet variance as a function of the measurement time. The spectrum is generally approximated by the `power law,' i.e., a Laurent polynomial with integer exponents of the frequency. This article extends the domain of application of PVAR, a wavelet variance which uses the linear regression on phase data to estimate the frequency, and called `parabolic' because such regression is equivalent to a parabolic-shaped weight function applied to frequency fluctuations. In turn, PVAR is relevant in that it improves on the widely-used Modified Allan variance (MVAR) enabling the detection of the same noise processes at the same confidence level in a shorter measurement time. More specifically, we provide (i) the analytical expression of the response of the PVAR to the frequency-noise spectrum in the general case of non-integer exponents of the frequency, and (ii) a useful approximate expression of the statistical uncertainty.
