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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Simulations of the Hadamard Variance: Probability Distributions and Confidence Intervals
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Simulations of the Hadamard Variance: Probability Distributions and Confidence Intervals

机译：Hadamard方差的模拟：概率分布和置信区间

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摘要

Power-law noise in clocks and oscillators can be simulated by Fourier transforming a modified spectrum of white phase noise. This approach has been applied successfully to simulation of the Allan variance and the modified Allan variance in both overlapping and nonoverlapping forms. When significant frequency drift is present in an oscillator, at large sampling times the Allan variance overestimates the intrinsic noise, while the Hadamard variance is insensitive to frequency drift. The simulation method is extended in this paper to predict the Hadamard variance for the common types of power-law noise. Symmetric real matrices are introduced whose traces—the sums of their eigenvalues—are equal to the Hadamard variances, in overlapping or nonoverlapping forms, as well as for the corresponding forms of the modified Hadamard variance. We show that the standard relations between spectral densities and Hadamard 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.
机译：时钟和振荡器中的幂律噪声可以通过傅立叶变换修改后的白相噪声频谱进行模拟。该方法已成功应用于重叠和非重叠形式的Allan方差和修改后的Allan方差的仿真。当振荡器中存在明显的频率漂移时，在较大的采样时间，艾伦方差会高估本征噪声，而哈达玛方差对频率漂移不敏感。本文扩展了模拟方法，以预测常见类型的幂律噪声的Hadamard方差。引入对称实矩阵，其迹线（其特征值的总和）等于Hadamard方差（重叠或非重叠形式）以及修改后的Hadamard方差的相应形式。我们表明，使用这种方法可以获得光谱密度和Hadamard方差之间的标准关系。矩阵特征值确定概率分布，用于观察采样间隔的任意值的方差，从而估计测量的置信度。

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