How to Deal with FFT Sampling Influences on ADEV Calculations

Po-Cheng Chang

Abstract:	We have done some work to reveal that Fast Fourier Transform (FFT) sampling may induce unreasonable Allan deviation (ADEV) values while the numerical integration is used for the time and frequency (T&F) conversion. These ADEV errors occur because parts of the FFT sampling have no contributions to the ADEV calculation for some t. For example, when averaging interval t = 0.004 (s) and Fourier frequency f = 250 (Hz), the term sin (ptf), which plays a key role in the mathematical conversion, is zero. If FFT sampling in a specific frequency range is only at multiples of 250 (Hz), spectral density in this range has no contributions to ADEV calculations for t = 0.004 × N (s), where N is a positive integer. Our lab has also found such errors in related commercial software. In order to solve this problem without skipping over effects from certain values of t, we try to change the original sampling data in several ways, like dividing sampling spaces into narrower ones or shifting the FFT sampling frequency a small amount, etc. The regenerated data using interposition techniquess are then calculated via the T&F conversion. According to our tests, the FFT sampling within logarithmic frequency space exceeds the others at reducing ADEV errors. As for spur effects, the spectral density with spurs is likely to double or triple ADEV values from the same density with spurs removed in our case, so it is meaningful for laboratories to reduce ac power and other periodic noises in their own environment. The power-law processes can also perform the T&F conversion and identify different noise types in the spectral density. ADEV results calculated from this way are in good agreement with those from the numerical integration.
Published in:	Proceedings of the 39th Annual Precise Time and Time Interval Meeting November 27 - 29, 2007 Hyatt Regency Long Beach Long Beach, California
Pages:	551 - 557
Cite this article:	Chang, Po-Cheng, "How to Deal with FFT Sampling Influences on ADEV Calculations," Proceedings of the 39th Annual Precise Time and Time Interval Meeting, Long Beach, California, November 2007, pp. 551-557.
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