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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Probability distributions and confidence intervals for simulated power law noise
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Probability distributions and confidence intervals for simulated power law noise

机译：模拟幂律噪声的概率分布和置信区间

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摘要

A method for simulating power law noise in clocks and oscillators is presented based on modification of the spectrum of white phase noise, then Fourier transforming to the time domain. Symmetric real matrices are introduced whose traces???the sums of their eigenvalues???are equal to the Allan variances, in overlapping or non-overlapping forms, as well as for the corresponding forms of the modified Allan variance. We show that the standard expressions for spectral densities, and their relations to Allan variance, are obtained with this method. The matrix eigenvalues determine probability distributions for observing a variance at an arbitrary value of the sampling interval ??, and hence for estimating confidence in the measurements. Examples are presented for the common power-law noises. Extension to other variances such as the Hadamard variance, and variances with dead time, are discussed.
机译：提出了一种在时钟和振荡器中模拟功率定律噪声的方法，该方法基于修改白相噪声频谱，然后进行傅立叶变换到时域。引入对称实矩阵，其迹线“它们的特征值之和”等于艾伦方差，呈重叠或非重叠形式，以及修正艾伦方差的相应形式。我们表明，使用这种方法可以获得谱密度的标准表达式及其与艾伦方差的关系。矩阵特征值确定概率分布，该概率分布用于观察采样间隔Δθ的任意值处的方差，并且因此用于估计测量中的置信度。给出了常见的幂律噪声示例。讨论了其他方差的扩展，例如Hadamard方差和死区时间方差。

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