THEORETICAL FUNDAMENTALS OF IMLSE TRANSMISSION 



740 



a;, 2a;, 



FREQUENCY 



Fig. 17 — Modification of frequency characteristic to obtain same response as 

 for impulses, when pulse duration is in-olonged to half the pulse interval. 



given by (5.03) 



Fit) = — ^ cos COmto 



sin cjmto 



5cOr 



sin 2o3mto 



(co„,^o/7r) -] 



(5.05) 



TT 2Umto[l — (o^mto/Tr)'^]' 



Pulses can in this case be transmitted witliout mutual interference be- 

 tween the pulse peaks at the points shown in the above figure. The 

 effective pulse transmission rate is the same as for a low-pass characteris- 

 tic between w = and co = 2a) ,„ with haK amplitude at co,„ .* 



As mentioned in Section 2, when pulses of finite duration are employed, 

 the same response as for impulses is obtained if the amplitude charac- 

 teristic is modified by the factor (co5/2)/sin (co8/2). In Fig. 17 is shown 

 the resultant minor modification in the amplitude characteristic (5.01) 

 when the duration of the pulses is equal to half the pulse interval. 



The low-pass and band-pass amplitude characteristics considered 

 above can also be regarded as the specti'a of pulses applied to a trans- 

 mission system ha^'ing a constant amplittide characteristic over the 



* W. R. Bennett and C. B. Feldniaii originally i)roposed this type of charac- 

 teristic in an unpuljlished memorandum, as a means of matching the bandwidth 

 economy of baseband transmission without inclusion of frequencies near zero. 



