THEORETICAL FUNDAMENTALS OF Pl^LSE TRANSMISSION 1007 



stantial reduction in delay distortion over the transmission band. This 

 is illustrated in Fig. 49, Avhere a co.sine variation in transmission delay 

 is assumed. With a two-fold reduction in bandwidth, the product 

 d'max/'max for vcstigial sideband transmission is about 15 per cent of the 

 product c/max/inax for doublc sideband transmission. Thus, with c?max/max 

 = 8.3, d'lnaxf max = 1-25, Corresponding to 6 = 5 radians, as assumed in 

 the example in Section 14. Vestigial sideband transmission is in this case 

 feasible with an adecjuate margin, about 40 per cent of the maximum 

 margin in the absence of phase distortion. Double sideband transmission 

 would not be possible, as is evident from Fig. 43, since it would be neces- 

 sary to have c^max/max Icss thau 4, as compared with 8.3 in the above case. 

 The above discussion of vestigial vs double sideband transmission 

 pertains to the effects of characteristic distortion rather than noise, and 

 the relative complexity of terminal equipment was disregarded. Because 

 of the simpler terminal equipment with double sideband transmission, 

 this method is ordinarily used w^here bandwidth is not a primary con- 

 sideration, as for example in providing a number of telegraph' channels 

 over a \'oice freciuency circuit. 



16. LIMITATION ON CHANNEL CAPACITY BY CHARACTERISTIC DISTORTION 



For an ideahzed channel of bandwidth /i with a transmission-frequency 

 characteristic as shown in Fig. 7, the transmission capacity in bits per 

 second for a signal of average power P in the presence of random noise 

 of average power N can with sufficiently complicated encoding methods 

 approach the limiting value given by Shannon :^^ 



C = /i log2 (1 -f P/N). (16.01) 



The above expression also appHes to certain other ideahzed channels 

 with a linear phase characteristic, w^hen /i is defined as in Fig. 10. In all 

 of these cases the integral of the area under the amplitude characteristic, 

 or the equivalent bandwidth, is /i . 



By way of comparison, for pulse code modulation systems the channel 

 capacity is of the same basic form as (16.01), namely : 



C = /:log2(n-^), (16.02) 



where K = 8. Thus about an 8-fold increase in signal power is required 

 to attain the same channel capacity as with the idealized but imprac- 

 ticable encoding system underlying (16.01). 



The above expressions give the limitation on channel capacity imposed 

 by random noise. From the discussion in Sections 13 and 14 it follows 

 that a limitation is placed on channel capacity by characteristic distor- 



