THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 



0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 



00/ 00^ OJc/UJ 



Fig. 3 — Low-pass transmission frequency characteristies with natural linear 

 pliase shift foi- w/wc < 1. 



linear phase characteristic in this range are of particular importance in 

 pulse transmission, this case will be considered further. 



Tt will be assumed that the phase characteristic has even symmetry 

 when expressed in the scales of Fig. 2, in which case the phase charac- 

 teristic as shown by the solid lines in Fig. 3 is given by 



V'"(") = ^T 



j/cOe < 1, 



(1.07) 



= coc r/co oi/(x)c > 1. 



With these expressions in (1.04) the attenuation characteristic becomes: 



(nA{o:) = 



1 + 



1 /a; 



Wc 



(ri 



1 + Cj/cJc ~| 

 1 — Oo/WcJ 



For CO = 0, the latter expression approaches the limit (nA{()) = 4ajcr/7r, 

 so that 



/'n.l(a;)A4(0) 





1 + 



1 



Z \Wc 



in 



1 



i/Wc_ 



(1.08) 



wliich is the attenuation characteristic shown in Fig. 3. 



Other attenuation characteristics with a linear phase characteristic 

 between co/wc = and 1 are possible with other types of variations in 

 the attenuation or phase characteristic for co/co, > 1 than assumed 

 above. For example, the attenuation characteristics may be assumed 



