378 BELL SYSTEM TECHNICAL JOURNAL 



the same tvave form; i.e. 



*(0 = Z (- l)'"am0m(^ - tm), 

 1 



<i>,n{t) = <A(/), < / < X;„ 



= / > x,„, 



/m = Xi + X2 + ' • • + X/n-l, 



and we denote the mean frequency of occurrence, NIT, by v. 



Substitution in the preceding formulas and straight-forward opera- 

 tions give 



R{o,)=-\ a\{a)da- \f{io:, \)\^-p{\)d\ 



^ Jo Jo 



— r rag(a)JaT- f'/O/co, X)^(X)e*"VX • f f{- iw,\)p{\)d\ 

 "■ L Jo J Jo Jo 



XLimi-^L L (-1)"-H p{\)e'-^d\\ . (10) 



If we write 



r p{\)e'-^d\ = p(ia>) = p, (11) 



Jo 



we have by straightforward procedure 

 Limi^E E (-1)"- ^(X).-VX = ^ , ., . , (12) 



jvr-^oo iV OT=1 n = m+l L Jo J ^ ^ Pl^'^'J 



whence 



7?(co) =-^ Pa2g(a)Ja f \f(io:, \)\'-p(\)d\ 



-Mra.^a^.al-l'Mlff] , (.3) 



TT L Jo J i 1 + P^^"^) J Real Part 



/(iw, X) = r <l>{t)e^"'dt = c(co, X) + w(a), X), 

 Jo 



£/(co) = rii'io:, X)/>(X)e^"VX. (14) 



Jo 



F(co) = rf{-ic^,\)p{\)d\. 



Jo 



where 



