The spectrum of modulated pulses

Some methods proposed for evaluating the spectra of modulated pulse trains are discussed. The basic pulse-frequency, -phase, -length and -amplitude modulation systems are defined and the spectrum of a train of rectangular pulses sinusoidally modulated in any one of these ways is derived. Modulation by more than one tone is also considered. It is shown that in none of these methods is there any harmonic distortion or audio crosstalk. Anharmonic distortion arises from sidebands of harmonics of the pulse repetition frequency, and graphs are given to illustrate its magnitude. The formulae are extended to cover non-rectangular pulses, and it is shown that the distortions to be expected are practically the same as for rectangular pulses. The reproduction of transients is briefly examined. It seems that they suffer little distortion in form but that their timing is modified by the pulse modulation, the maximum time-shift being half the pulse repetition period.