SPECTRUM ANALYSIS OF WAVES 



381 



AZ,,„) recurring every l/v seconds will be a Fourier series of harmonics of v. 

 The amplitude of the nth term of this series will be 



J^n = 77. — sm 



TTll 



1 + ^ sin 



27rw 



lo" 



This expression may be found from appendix C, equation (5a). Combining 



^ 0.6 



40 50 60 70 



MODULATION IN PER CENT 



Fig. 11 — Spectrum of pulse width modulated wave for case where carrier frequency C is 

 10 times the signal frequency v. 



the 10 such components at each frecjuency, as shown on Fig. 7 for the case 

 of the pulse position modulated wave, the spectrum for this case of Pulse 

 Width Modulation on Fig. 11 is produced. This spectrum is comparable 

 to that on Fig. 8 for the pulse position modulated case. 



Pulse Width vs Amplitude Modulation 



That pulse width modulation is a form of amplitude modulation of the 

 carriers of the unmodulated pulse train is shown mathematically by Equa- 



