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BELL SYSTEM TECHNICAL JOURNAL 



in the single pulse spectrum. This gives a spectrum like that shown on 

 Fig. 6. Figure 6 also shows for comparative purposes the spectrum of the 

 subsidiary pulse wave consisting of every 6th pulse. 



Thus in the unmodulated case, the pulses have a uniform recurrence rate 

 and the resultant spectrum, found by adding those of the individual pulses, 

 reduces to a train of discrete frequencies comprised only of the harmonics of 

 the recurrence rate of the pulses. The fundamental frequency, correspond- 



1.0 



2 0.8 



0.6 

 0.4 



0.2 



C 2C 3C 4C 50 



FREQUENCY, f, IN TERMS OF C (WHERE C =!/j) 



WHERE PULSE LENGTH = 1/36 PERIOD LENGTH 



FREQUENCY SPECTRUM 



TITTTITfTTITrTTrrn-rTT-n-T-r.-r 



2V 4V 6V 8V lOV 12V 18V 24V 30V 



FREQUENCY, f, IN TERMS OF V (WHERE V = l/gC = l/gT) 



36V 



Fig. 6 — Frequency spectrum of pulse trains where the spacing between the pulses is 6 and 

 36 times the pulse length respectively. 



ing to the recurrence rate, and its harmonics will be called the carrier fre- 

 quencies of the pulse train. The effect of modulating the pulse train is to 

 modulate each of these carriers, producing sidebands of the signal about 

 them. 



When the pulse train is position modulated, the pulses are shifted in posi- 

 tion by an amount AT, corresponding to the instantaneous ami^litudes of 

 the modulating function. The spectrum of each pulse is unchanged, since 

 the pulse length remains constant. However, components of successive 



