Article | REF: R681 V1

Time and frequency stability of oscillators: analysis tools

Author: François VERNOTTE

Publication date: June 10, 2006

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1. Variances

Statistical methods are generally used to study random phenomena. In the case of Gaussian noise, two quantities suffice to define its probability law: the mean value and the variance . It is the variance, of course, that will enable us to characterize oscillator instabilities.

1.1 True variance

Let's consider a sequence of samples of normalized instantaneous frequency deviation, which we assume to be stationary and ergodic. Let's denote I 2

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Variances