Hi How to treat a negative is up to you, it's obviously indicating a "not real" outcome. Zero is also a "not real" for realizable oscillators. Most simply note the result as "below floor", drop it, and proceed.
Since the variability of the data is driving the negative results, it's unlikely that another approach will massively improve things (with the same data set). The practical answer is to use oscillators with closer noise performance to reduce the scatter or to improve the data collection method if it's the limiting factor. Bob -----Original Message----- From: time-nuts-boun...@febo.com [mailto:time-nuts-boun...@febo.com] On Behalf Of Kyle Wesson Sent: Thursday, April 22, 2010 5:07 PM To: time-nuts@febo.com Subject: [time-nuts] Frequency Stability of An Individual Oscillator:Negative Values? Hello, I am working to determine the Allan variance of an individual oscillator from a series of three paired measurements as described in the paper by Gray and Allan "A Method for Estimating the Frequency Stability of An Individual Oscillator" (NIST, 1974, tf.nist.gov/general/pdf/57.pdf). In this report they make reference to the statistical uncertainty of the measurement due to ensemble noise and potential clock phase correlation which can potentially make the Allan variance for an individual oscillator have a negative value. They write: "If the noise level of the oscillator being measured is low enough, and the scatter high enough, equation (4) may occasionally give a negative value for the variance." My question is: how should I treat negative variance values in this case? For example, if my data set were to produce an individual oscillator Allan variance with a value of -5e-12, should I convert this value to 0 (ie. the closest valid sigma value to the number since 0 <= sigma < inf ), take the absolute value of the result (ie. turn -5e-12 to +5e-12), or drop the result from my estimate of individual oscillator frequency stability altogether? Is there another method that will produce estimates of individual oscillators from an ensemble approach but assures non-negative output variances? Thank you in advance, Kyle _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
