The 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 with the “power law,” i.e., a Laurent polynomial with integer exponents of the frequency. This article provides: 1) the analytical expression of the response of the wavelet variance parabolic variance (PVAR) to the frequency-noise spectrum in the general case of noninteger exponents of the frequency and 2) a useful approximate expression of the statistical uncertainty. In turn, PVAR is relevant in that it replaces the widely used modified Allan variance (MVAR), featuring the identification of noise processes with fewer data.

中文翻译：

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抛物线方差 PVAR 对幂律非整数指数的响应和不确定性


振荡器波动被描述为相位或频率噪声谱或根据作为测量时间的函数的小波方差。频谱通常用“幂律”近似，即具有频率整数指数的洛朗多项式。本文提供：1) 在频率非整数指数的一般情况下，小波方差抛物线方差 (PVAR) 对频率噪声谱响应的解析表达式；2) 统计不确定性的有用近似表达式。反过来，PVAR 的相关性在于它取代了广泛使用的修正艾伦方差 (MVAR)，其特点是用更少的数据识别噪声过程。