Journal ArticleDOI
Statistics of atomic frequency standards
David W. Allan
- Vol. 54, Iss: 2, pp 221-230
Reads0
Chats0
TLDR
In this paper, a theoretical analysis of the relationship between the expectation value of the standard deviation of the frequency fluctuations for any finite number of data samples and the infinite time average value of a standard deviation is presented.Abstract:
A theoretical development is presented which results in a relationship between the expectation value of the standard deviation of the frequency fluctuations for any finite number of data samples and the infinite time average value of the standard deviation, which provides an invariant measure of an important quality factor of a frequency standard. A practical and straightforward method of determining the power spectral density of the frequency fluctuations from the variance of the frequency fluctuations, the sampling time, the number of samples taken, and the dependence on system bandwidth is also developed. Additional insight is also given into some of the problems that arise from the presence of "flicker noise" (spectrum proportional to |ω|-1) modulation of the frequency of an oscillator. The theory is applied in classifying the types of noise on the signals of frequency standards made available at NBS, Boulder Laboratories, such as: masers (both H and N15H 3 ), the cesium beam frequency standard employed as the U. S. Frequency Standard, and rubidium gas cells. "Flicker noise" frequency modulation was not observed on the signals of masers for sampling times ranging from 0.1 second to 4 hours. In a comparison between the NBS hydrogen maser and the NBS III cesium beam, uncorrelated random noise was observed on the frequency fluctuations for sampling times extending to 4 hours; the fractional standard deviations of the frequency fluctuations were as low as 5 parts in 1014.read more
Citations
More filters
Journal ArticleDOI
Estimating the Allan variance in the presence of long periods of missing data and outliers
Ilaria Sesia,Patrizia Tavella +1 more
TL;DR: This work proposes an estimation algorithm and its implementation in a robust software code (in MATLAB® language) able to estimate the AVAR in the case of missing data, unequally spaced data, outliers, and with long periods of missing observation so that the Allan variance estimates turn out unbiased and with the maximum use of all the available data.
Journal ArticleDOI
Rhythm in speech and animal vocalizations: a cross-species perspective
Andrea Ravignani,Andrea Ravignani,Simone Dalla Bella,Simone Falk,Christopher T. Kello,Florencia Noriega,Sonja A. Kotz,Sonja A. Kotz +7 more
TL;DR: The literature on rhythm in speech and animal vocalizations is reviewed as a first step toward understanding similarities and differences across species and quantitative techniques that are useful for computing rhythmic structure in acoustic sequences are extended to facilitate cross‐species research.
Journal ArticleDOI
Allan variance of time series models for measurement data
TL;DR: In this article, the authors provide a statistical underpinning of the Allan variance for discrete stationary processes, random walk and long-memory processes such as the fractional difference processes including the noise models usually considered in time and frequency metrology.
Journal ArticleDOI
On Improving Navigation Accuracy of GPS/INS Systems
TL;DR: In this paper, the authors focused on three error modeling and compensation techniques that could potentially improve GPS/INS system performance on both land-based and airborne platforms: (1) extended gravity compensation, (2) IMU signal de-noising, and (3) stochastic modeling of IMU errors.
Proceedings ArticleDOI
On the measurement of frequency and of its sample variance with high-resolution counters
TL;DR: Rubiola et al. as mentioned in this paper showed that feeding a file of contiguous data into the formula of the two-sample (Allan) variance sigmay 2(tau) = E{frac12(ymacrk+1-ymACrk)2} gives the modified Allan variance mod sigmay 1 (tau).
References
More filters
Journal ArticleDOI
An Introduction to Fourier Analysis and Generalized Functions.
R. A. Kunze,M. J. Lighthill +1 more
TL;DR: The theory of generalised functions and their Fourier transforms is discussed in this paper. But the analysis of Fourier transform is limited to the case of generalized functions, and it is not suitable for generalised function analysis.
Journal ArticleDOI
Some aspects of the theory and measurement of frequency fluctuations in frequency standards
Leonard S. Cutler,C. L. Searle +1 more
TL;DR: In this article, the effects of finite observation time on the frequency and phase stability of a servo-controlled oscillator with respect to a given quartz oscillator and an atomic reference are analyzed.
Journal ArticleDOI
Atomic timekeeping and the statistics of precision signal generators
TL;DR: In this paper, a detailed analysis of the calibration procedure showed that the third finite difference of the phase is closely related to the clock errors and that quartz crystal oscillators exhibit a "flicker" or |ω|-1type of noise modulating the frequency of the oscillator.
Atomic timekeeping and the statistics of precision signal generators
TL;DR: The method of finite differences of the phase is shown to be a powerful means of classifying the statistical fluctuations of thephase and frequency for signal generators in general and by employing finite differences it is possible to avoid divergences normally associated with flicker noise spectra.
Related Papers (5)
The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS)
Peter Werle,R. Mücke,F. Slemr +2 more