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TheoH and Allan Deviation as Power-Law Noise Estimators



Jennifer A. Taylor, David A. Howe


A spectral interpretation using the frequency response of the Allan Variance is used to determine slopes of fα noise, commonly called ''power-law noise.'' This paper shows that TheoH provides significantly better determination of fα noise slopes at long-term. By calculating confidence intervals with a chi-square distribution for TheoH and the Allan Variance (Avar), we find that TheoH has narrower confidence than Avar. TheoH has even narrower confidence than chi-square, but the algorithms used to calculate these confidence intervals are long and computationally intensive. We have constructed an empirical formula that approximates the percent error for TheoH and is much more convenient to use in a measurement situation for an accurate estimate of confidence. Because of the narrow confidence, TheoH determines a particular slope at long-term, and we show the comparison to Avar.
IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control


Allan deviation, confidence, frequency stability, long-term, noise, oscillator, spectrum, TheoH, variance


Taylor, J. and Howe, D. (2007), TheoH and Allan Deviation as Power-Law Noise Estimators, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, [online], (Accessed June 22, 2024)


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Created January 31, 2007, Updated October 12, 2021