Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Probability distributions and confidence intervals for simulated power law noise

Published

Author(s)

Neil Ashby, Bijunath Patla

Abstract

Simulation of 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. This approach has been applied successfully to simulation of the Allan variance and the modified Allan variance in both overlapping and non-overlapping forms. The simulation method is extended in this paper to predicting 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 non-overlapping 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. The matrix eigenvalues determine probability distributions for observing a variance at an arbitrary value of the sampling interval τ, and hence for estimating confidence in the measurements. Examples are presented for the common power-law noise.
Citation
IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control
Volume
62
Issue
1

Keywords

ADEV, Allan variance, Hadamard variance, power law noise, simulation

Citation

Ashby, N. and Patla, B. (2015), Probability distributions and confidence intervals for simulated power law noise, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, [online], https://doi.org/10.1109/TUFFC.2013.006167 (Accessed May 25, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created January 12, 2015, Updated November 10, 2018