THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 



■87 



tratcil in Fig. 41. For a specified pulse overlap or iiitersyinl)()l inlerfereiu'e 

 the pulse spacing must accordingly l)e increased by the factor ti/d, , so 

 that for a given transmission performance the transmission capacity is 

 retlucetl by the factor (o/d . About the same effect would be expected for 

 other pulse shapes or amplitude characteristics resembling the (laussian 

 shape assumed in the above deriA-ation. 



Comparison of (11.08) with (2.13) shows that the function (^(/) with 

 respect to the midband frequency is 



^(0 = e - hr. (11.13) 



If the reference or carrier fre(iuency is displaced from the midband by 



AMPLITUDE CHARACTERISTIC 



FREQUENCY 



— ^ DELAY DISTORTION 

 (a) TRANSMISSION FREQUENCY CHARACTERISTIC 



WITHOUT DELAY DISTORTION-,/ 



■\WITH DELAY DISTORTION 



(b) IMPULSE CHARACTERISTICS WITHOUT AND WITH DELAY DISTORTION 



t, =to[l + 0.46(d^^^f^^,f]2 



^MAX = FREQUENCY FROM MIDBAND AT WHICH AMPLITUDE OF TRANSMISSION 

 FREQUENCY CHARACTERISTIC IS REDUCED 40 DECIBELS 



^MAX = DELAY DISTORTION AT f^^X IN SECONDS 



Fig. 41 — Lengthening of impulse envelope l)y linear delay distortion for 

 Gaussian transmission characteristic. 



