786 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



The real and nesati\e imaginary components of this expression are 

 /?_ + R+ = 25 (^\" e-"'" cos (6 - U'), and 



Q_ - Q+ = 25 p j e-"'" sin (6 - hf), 

 where 



tan 29 = 0/a = 6/a 

 The impulse characteristic obtained with (11.07) in (2.09) becomes 



p(t) = 25 (-\" e-"'" [cos (a^rt - 4^r) cos (6 - br) 



^^/ (11.08) 



+ sin (cort — \pr) sin (9 — bf)]. 



From (11.08) it is seen that the envelope is 



P(t) = 25 (-\ e^"'". (11.09) 



The peak of the envelope obtained with ^ = is smaller than Avithout 

 delay distortion (^ = 0) by the factor 



^ (11.10) 



1 + i^/ayv' 



The constant a is smaller than without delay distortion by the factor 

 77 . If ^0 designates the time required for the instantaneous amplitude of a 

 pulse to decay from its peak to a given value ^nthout delay distortion, 

 the time ^1 to reach the same amplitude with delay distortion is 



^1 = t,/rf = toil + (^/a)T\ (11.11) 



If Wniax indicates the frec^uency at the 40 db down point on the trans- 

 mission frequency characteristic, acomax" = 4.6. The corresponding delay 

 distortion is f/max = 2a),„axiS. Thus l3/a = .68 c?,„ax/max so that (11.11) 

 becomes : 



k = ^o[l + 0.40 (f/„.ax/max)T''. (11-12) 



The effect of a linear delay distortion across the transmission band is 

 thus to disperse or broaden the envelope of the received pulses, as illus- 



