MATHEMATICAL AX A LYSIS OF RANDOM XOISE 



103 



of the instantaneous values of /.v. When av » 1 and (7 » v — a | we may 

 expand the coefficient of the exponential term in (3.10 19) in powers of 



Fig. 7 — Distribution function of envelope R of 7(0 = P cos pi + /.v 



{v - a)/ a. Integrating this expansion termwise gives, when terms of magni- 

 tude less than a"^ are neglected, 



1 1 V — a 



r 1 1 t> — I 



2a\/2x _ 



1 - 



4a 



a 1 + (z) — a)-' 



8a- 



exp 



(v - a)n 



