THEORETICAL FUNDAMENTALS OF PULSE TRANSMLSSION 1009 



or 



U'- = J) = N/P. (10.08) 



This means that random characteristic cHstortion has the same effect 

 as a random noise power N = DP, where Z) is a distortion factor. 



In view of the above equivalence, the channel capacity of a PCM 

 system in the presence of random characteristic distortion, but without 

 noise, as obtained by substitution of (1G.08) in (16.02) becomes 



C = /i log, (l + ]^) • (10.09) 



With random interference from both characteristic distortion and noise, 

 the interfering powers add directly, so that for a PCM system 



''-f^'A' + mTNjp))- ^'"'"^ 



The equivalence (16.08) was established above on the liasis of discrete 

 pulse amplitudes, but it is independent of q and would thus apply also 

 for continuous signals. On this basis it would apply for an^^ method of 

 modulation or of encoding signals and the maximum channel capacity 

 as given by (16.01) would be modified to 



It follows from the above that for any modulation method the toler- 

 able distortion factor is directly related to the average signal-to-noise 

 ratio. Thus two modulation methods which are equivalent from the 

 standpoint of signal-to-noise ratio are also equi\'alent from the standpoint 

 of tolerable rms distortion, provided faithful reproduction of the trans- 

 mitted signal is required, as assumed here. 



From (8.14) the following relation is obtained between the distortion 

 factor D = U^ and small rms deviations a (nepers) and b (radians) in the 

 amplitude and phase characteristics 



D = or -\- b\ (16.12) 



In order that characteristic distortion may be disregarded in compari- 

 son with noise, it is necessary that D <5C N/P or 



a' + &' « N/P. (16.13) 



For example, in communication systems employing the same band- 

 width as the original signal, such as a pulse amplitude modulation sys- 

 tem, a representative signal-to-noise ratio would be about 40 db, or 

 N'/P = 10~*. In order that characteristic distoition may ])C disregarded 

 in this case, it would be necessary for both a and b to be substantially 



