764 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



frequency characteristic is in this case 



rr(^ \ rp ( ^ \ a (coswT— tsin ojt) 



= ro(tco)e , 



2 3 



l+a6 +-e +3^6 + 



(7.12) 



= ro(ico) 



The modified impulse characteristics is in this case 



P(0 = Po(0 + an(< - ^) + ^ ^o(^ - 2r) 



+ I Po(^ - 3r) + 



(7.13) 



For small values of a both (7.11) and (7.13) give for the modification 

 in the impulse characteristic resulting from a small cosine deviation in 

 the amplitude or attenuation characteristics accompanied by changes 

 in the phase characteristic: 



P(0 = Po(0 + a Po(^ - r). (7.14) 



In certain appUcations it is convenient to regard Po(0 as a pulse or 

 signal apphed to a transmission line and P(0 as the received pulse or 

 signal w\\h a cosine deviation in the amplitude characteristic of the 

 transmission line. 



In the lower part of Fig. 28 is sho■^^'n the modification in the received 

 pulses resulting from a slow pronounced cosine deviation in the ampli- 

 tude characteristic shown at the top. In Fig. 29 is showTi the effect of 

 positive and negative cosine variations when the ampHtude at zero fre- 

 quency is held constant, a condition which may be approximated in wire 

 systems as a result of variation in attenuation over the transmission 

 band with temperature. Curve 1 would correspond to a 3.5 db smaller 

 loss at the maximum frequency 2wi than at zero frequency, and curve 2 

 to a 6 db greater loss at the maximum frequency. It will be noticed that 

 pulse distortion as well as the variation in the peak amplitude of the 

 pulses is greater under the first condition, i.e. curve 1. Pulse overlaps can 

 in both cases be avoided by a moderate increase in pulse spacmg, and 

 in the first case can be substantially reduced also bj' a decrease in pulse 

 spacing. 



8. FINE STRUCTURE IMPERFECTIONS IN TRANSMISSION CHARACTERISTICS 



As a result of imperfections in the transmission medium and in equali- 

 zation there may be fine structure departures from a nominal transmis- 

 sion characteristic, as illustrated in Fig. 30. They are often caused by 



