TIME DIVISION MlLTiri.EX SYSTEMS 



205 



T/N allotted to that channel and breaks contact throughout the remainder 

 of the switching cycle, we may write the reference switching function as: 



Hence from (4) 



A, -xT/2n < t < xTllN 



0, xTIlN < t < (IN - x)T/2N 



A 01 = Ax/N, 



2.4 . mxir 

 A„,i = — sm — — , w > 

 niTT DJ 



dm\ = 



(17) 



(18) 



In the receiving device, the corresponding switching process should be 

 delayed with respect to the transmitter by a time interval /o equal to the 

 time of transmission of the line. Hence we write 



Box - Bx/N 



\ 



2B . mxTT [ 



mir N 



<^mi = mqto 



(19) 



B,ni and dmj are related to B^i and $,„! in a manner analogous to (16). 



The time of transmission of a distorting line is not precisely definable, 

 but may be represented for our purpose by a linear phase component of 

 Z(/co). That is, we write 



Z(/co) = Zo{i(j})e 



— ito<' 



(20) 



where io is the slope of a straight line giving the best linear approximation 

 to the phase vs. frequency curve, and Zo(/co) is the impedance function 

 remaining after the subtraction of /oco from the actual phase shift ordinates. 

 Substituting (15)-(19) in (12), we find 



Yik = A Be' 



N- 



Zoiiuij) 



+ E 



7n=l 



sin mx-w/N 



Zo[i{mq + ccj)]e 



-i{j-k)'lmirlN 



+ 2^ ^ / Zo{i{mq - coy)Jc 1 (21) 



