THEORETICAL FUXDAMEXTALS OF PULSE TRANSMISSION 



751 



5 



< 0.5 



-0.4 -0.2 0.2 0.4 0.6 0.8 I.O 1.2 1.4 1.6 1.8 2.0 2.2 



'tofMAX - 2tof) 



Fig. 18 — Comparison of two representative frequency and impulse transmis- 

 sion characteristics. Frequency characteristic 1 : T{ui) = ^[l -(- cos 7rc<;/2wi]. Fre- 

 quenc}' characteristic 2: T'(co) = e.xp — 0.54(co/a)i)2. 



Amplitude characteristic 1 of Fig. 18 has certain properties, aside 

 from the linearity of the associated phase characteristic, which makes it 

 preferable to a Gaussian as well as other types of amplitude characteris- 

 tics for most pulse systems. The corresponding impulse characteristic 

 has zero points at intervals n = l/2/i with the minimum possible oscilla- 

 tion consistent with this property for a given bandwidth. This permits 

 the use of this impulse characteristic for pulse systems with discrete 

 pulse positions with minimum intersymbol interference and considerable 

 tolerance on synchronization. Since the oscillation in the impulse char- 

 acteristic is inappreciable, it can also be used for pulse systems without 

 discrete pulse positions and with other methods of detection than syn- 

 chronized instantaneous sampling. In view of these attributes, an ampli- 

 tude characteristic of the above type, rather than a constant amplitude 

 characteristic with sharp cut-off, may be regarded as ideal when various 

 physical requirements for practicable pulse systems are taken into con- 

 sideration. 



