782 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



be written: 



U = I ^^ ~ " Y "-TOO, and (10.07) 



COi 



F(/3i) = 2 



1/2 



1/2 



^-H^J ''^ + -^' 



1/2 



(10.08) 



For ^'ariolls values of the maximum phase deviation /3i in radians the 

 function F becomes: 



If, for example, phase distortion were confined to 10 per cent of the 

 transmission band, then (wi — co')/wi = 0.1. For a maximum phase 

 deviation of 1 radian at the edge of the transmission band, F = 0.43 and 

 U = 0.135. For a maximum phase distortion of 4 radians, F = 1.24 and 

 U = 0.39. Since peak intersymbol interference may exceed the above 

 rms values by a factor of about 3, and the maximum tolerable peak 

 intersymbol interference in a system employing two pulse amplitudes 

 would be less than 1, it is evident that band-edge phase deviations must 

 be held at rather small values, less than about 3 radians, in the upper 

 10 per cent of the transmission band. 



The above severe tolerances on band-edge phase distortion can be 

 overcome by employing a transmission frequency characteristic of the 

 type shown in Fig. 38 and previously discussed in Section 5. If the phase 

 characteristic is linear between co = and wi , and phase distortion 

 between coi and 2coi varies as 



^ = 01 



2coi — wi 



= /3i 



1-^ 



(10.09) 



equation (10.04) can be written 





1 + cos 



2coi 



1 - cos ^1 1 - 



0)1 



do), 



(10.10) 



1 — sin -z u) (1 — cos 3iU~) du. 



Pulses may also in this case be transmitted at intervals n = tt/wi 

 without intersymbol interference in the absence of phase distortion, so 



