PROPERTIES OF SINE WA VE PLUS NOISE 



149 



In these equations T^iv(/) is obtained from (8.7), and W2(f) by two-fold 

 integration by parts to reduce g" to g then evaluating the integral obtained 



0.70 



0.65 



0.60 



0.55 



0.50 



0.45 



0.35 



0.30 



0.25 



0.15 



0.05 



Fig. 8 — Power spectrum of dO/dt. 

 Power spectrum of /at is assumed to be 



U<rV2^r' exp [ - (/ - A)V(2a^)]. 



In this expression /is a frequency near/, . The/ in W(J) and in the abscissa is a much 

 lower frequency. W(f) = power spectrum of 6' = dd/dt, d' being regarded as a random 

 noise current. Dimensions of W(f)df same as (dd/dty or (radians)Vs€c.2. 



by substituting the expression (8.2) for g. That W(f) approaches Wzif) 

 as p — > =c follows when expression (8.11) for W2if) is compared with the 

 limiting form (8.13) given below. 



