The Fractal Dimension of Phase and Frequency Noises: Another Approach to Oscillator Characterization

An e v a l u a t i o n i s made o f t h e p o s s i b i l i t y o f a p p l y i n g M a n d e l b r o t ' s c o n c e p t o f f r a c t a l s t o t h e c h a r a c t e r i z a t i o n o f no ises and i n p a r t i c u l a r of phase and $requency f l u c t u a t i o n s . Two methods are considered. The f i r s t one c o n s i s t s i n m e a s u r i n g w i t h a gauge t h e appar e n t l e n g t h o f t h e s i g n a l : t h e f r a c t a l d i m e n s i o n o f w h i t e and random walk no i ses a re ca l cu la ted with this method. The second one i s based on the space f i l l i n g a b i l i t y o f t h e s i g n a l . The method i s a p p l i e d t o l / f a noises, which are s imulated on a computer, by superpos i t i o n o f l o r e n t z i a n s p e c t r a , f o r i n t e g e r and m inte g e r v a l u e s o f t h e c o e f f i c i e n t a . The dependence nf the f r a c t a l d i m e n s i o n D as a f u n c t i o n o f t h e spectral dms i t y i s es tab l i shed.