MULTICHANNEL MODULATION SYSTEM 



11 



determined in the presence of noise and interference. This spaces the sinus- 

 oidal pulses so that they overlap at their half-value points as illustrated in 

 Fig. 5c. There it will be observed that no matter how many pulses occur in 

 succession, the maximum amplitude of the pulse train is no different from that 

 of a single pulse. The spectra of all such pulse trains have a common envelope, 

 shown dashed in Fig. 5c. 



2. OFT 



1.5FT 



Fig. 5. Pulse forms and their associated amplitude spectra for: a, rectangular pulse; 

 b, single lobe of a sinusoidally varying pulse; c, succession of pulses, each like that in (b). 



Further, the band needed to transmit any sequence of such pulses is the 

 same as that needed for a single pulse. This can readily be shown by using 

 the familiar relation between transient build-up time and band width. More- 

 over, this conclusion is consistent with statistical analysis of all possible pulse 

 combinations, which yields a spectrum of the form of Fig. 5b. 



The relation between pulse duration and band width here described gives 

 close to the optimum ratio of signal to noise and interference for the system 

 considered. Narrowing the band would increase build-up and decay times, 

 leading to reduced pulse amplitude and to increased pulse overlap. Thus, 



