By James A. Barnes
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In t h i s example, one could l e t z t model the frequency of an o s c i l l a t o r , and i t i s c l e a r l y s t a t i o n a r y [12]. To model the phase, one could d e f i n e a parameter v t by the relation ( 1 - $'B)Vt = Z (B-12) t where __ l - + O i s l a r g e compared t o any data sample t o be t e s t e d . 002. 99999 t o be q u i t e adequate. Note t h a t vt i s a l s o s t a t i o n a r y . 99999 one obtains a s t a t i o n a r y model f o r vt i f one so d e s i r e s . Of course, f o r a c t u a l l y generating a data set one could use 4' = 1 , s i n c e no observational d i f f e r e n c e in t h e simulated data would r e s u l t - - t h a t i s why was chosen a s @ I c l o s e t o unity as i t was.
6] Lindsey, W . C . , Chie, C. M . , Theory of o s c i l l a t o r i n s t a b i l i t y based upon s t r u c t u r e functions. To be published. [7] Rutman, J . , Characterization of frequency s t a b i l i t y : A t r a n s f e r function approach and i t s application t o measurements via f i l t e r i n g of phase noise, I E E E Trans. on I&M, IM-23, No. 1 , pp. 40-48 (March 1974). [8] Lesage, P . , Audoin, C . , Characterization of frequency s t a b i l i t y : uncertainty due t o the f i n i t e number of measurements, IEEE Trans.
289-298 (April 1967). [20] Barnes, J . A . , Allan, 0. W . , A s t a t i s t i c a l model of f l i c k e r noise, Proc. I E E E , vol. 54, No. 2 , pp. 176-178 (Feb. 1966). [21] Barnes, J . A . , J a r v i s , S . , E f f i c i e n t numerical and analog modeling of f l i c k e r noise processes, NBS Tech. Note 604 (June 1971). [22] Wilson, R . G . , Prediction of phase (time) e r r o r s in oscillator-driven clocks, Aerospace Report No. TOR, 0075 (5461-04)-1 , The Aerospace Corp. (June 1975). [23] Mealy, G.
