Frequency Domain Stability Measurements
Frequency Domain Stability Measurements

Author: David A. Howe

Publisher: Forgotten Books

Published: 2018-08-21

Total Pages: 34

ISBN-13: 9781391539164

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Excerpt from Frequency Domain Stability Measurements: A Tutorial Introduction Frequency stability is the degree to which an oscillating signal produces the same value of frequency for any interval, At, throughout a specified period of time. Let's examine the two waveforms shown in figure 3. Frequency stability depends on the amount of time involved in a measurement. Of the two oscillating signals, it is evident that 2 is more stable than i from time t1 to t3 assuming the horizontal scales are linear in time. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Time Domain Frequency Stability Estimation Based On FFT Measurements
Time Domain Frequency Stability Estimation Based On FFT Measurements

Author:

Publisher:

Published: 2004

Total Pages: 7

ISBN-13:

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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 powerlaw 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.