Time Domain Frequency Stability Estimation Based on Fft Measurements

P.C. Chang, H.M. Peng, S.Y. Lin

Abstract:	The standard characterizations of frequency stability are, in the time domain, the Allan (or two-sample) variance and, in the frequency domain, the spectral density function (SDF). The former is mathematically related to the latter by the conversion between time and frequency domain. In this paper, the biases of the Fast Fourier transform (FFT) spectral estimate with Hanning window are checked and the resulting unbiased spectral density are used to calculate the Allan variance. Both the numerical integral and the curve-fitting methods are presented to calculate the variances. The numerical integral is a straightforward method to use, and we can get the integral approximation after eliminating some spike points from SDF, e.g. noise caused by ac power. In addition, a common model for SDF is linear combinations of power-law processes, which are distinguished by the integer powers in their functional dependence on Fourier frequency with the appropriate coefficients. Fitting a form of the above model to the resulting SDF using standard regression techniques can estimate these coefficients. Cutler’s formula is adopted to calculate the integral approximation using these coefficients. The approximations of variances from these two methods are compared and analyzed. Finally, we discuss the limitations and possible errors from these two methods.
Published in:	Proceedings of the 35th Annual Precise Time and Time Interval Systems and Applications Meeting December 2 - 4, 2003 Hilton Resort on Mission Bay San Diego, California
Pages:	261 - 266
Cite this article:	Chang, P.C., Peng, H.M., Lin, S.Y., "Time Domain Frequency Stability Estimation Based on Fft Measurements," Proceedings of the 35th Annual Precise Time and Time Interval Systems and Applications Meeting, San Diego, California, December 2003, pp. 261-266.
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