Spectrum Analysis of Pulse Modulated Waves

The rapidly expanding use of pulse modulation 1 in its various forms is bound to make the frequency spectrum of pulse modulated waves a subject of increasing practical importance. The purpose of this paper is to show how to determine the frequency spectrum of these waves by methods based as far as possible on physical rather than mathematical considerations. The physical approach is used in an attempt to maintain throughout the analysis a picture of the way in which the various factors contribute to a given result. To further this objective the fundamentals involved are reviewed from the same point of view. The method is used here to analyze two distinct types of pulse modulation, namely, pulse position and pulse width modulation. 2 These two cases are especially important for illustrative purposes because their spectra can be tied back to more familiar methods of modulation. Thus it will be shown that, as the ratio of the pulse rate to the signal frequency becomes large, pulse position modulation becomes a phase modulation of the various carrier frequencies that form the frequency spectrum of the unmodulated pulse wave, and pulse width modulation becomes a form of amplitude modulation of its equivalent carriers. The analysis also shows certain interesting inputoutput relationships that may be obtained from such modulators, treating them as straight transmission elements at the signal frequency. These relationships are of more than theoretical interest. The pulse position modulator has already been used as phase or frequency modulator to good advantage.