664 



BELL SYSTEM TECHNICAL JOURNAL 

 TABLE I (Continued) 



Pair 

 No. 



109. 



110.* 



111.^ 



112. 



Coefficient FU) for the 

 Cisoidal Oscillation 



- (Xo + Xi^ + X2^' + •••), 



< o < 1, lim by 501 



limby518=' 



■^ (Xo + \lP + X2^2 + X3^' +•••), 



lim by 502 ' 



Xo0o(/) + Xx0l(/) + X2<^2(/) + 



Coefficient G{g) for the 

 Unit Impulse 



+ X2(1 -a){2 -a)-+ "A, 0<| 



1 Tx 4-X ^^+X^' 

 :^|_Xo + X: ^ +X2 J. 3 



+ X3 



1.3-5 



+ 



]• 



<| 





1 . 1-3 

 1-3-5 



Xo - ^1 2g "^ ^' (2g)2 



+ •••], 0<i 



Xo</)o(g) + ^'XK^iCg) + i^^2<l>2(g) + • • • 



^' (2g)^ 



2 From (202) or (203), with g (or/) = 0, and (215) and (217) follow the important identities for th, 

 integrated product of two pairs of coefficients and for the integrated squared moduh of a pair ot coetticients 



r F,{f)F,{±f)df= r Cdg)G,{T g)dg, 



r \F-\df=r \C'\dg, 

 «y— 00 ^ — 00 



r* F,ix)G2{x)dx = r* Gi{x)F2{x)dx. 



«/— 00 »/— 00 



The symmetry of these identities is to be noted; this would not be the case if the radian frequenc; 

 2ir/ were employed in place of the cyclic frequency f. 



* A star marks a pair as being the limit approached by regular pairs. 



