Theoretical Study of Pulse-Frequency Modulation

In this paper, we study the pulse-frequency modulation method in pulse communication. We do not restrict ourselves to the case when the number of samples per period of our signal, as well as per unit time, is very large. Hence, the accuracy in reconstruction of the signal will depend not only on the number of sampling points per period, but also upon their distribution. We shall assume a fixed average pulse frequency (sampling rate), and will seek the maximal range of the signal frequency for which the corresponding periodic signal may be transmitted with acceptable accuracy. Thus, we are interested in a kind of threshold problem. It is our aim to consider pulse-frequency modulation independently of the circuits used to realize it, inasfar as this is consistent with lucidity of presentation. In Sections 12, 15, 16, and 17, we study in detail the behavior of sampling in case the relative frequency v (the ratio of the signal frequency to the pulse frequency) falls into the ranges (0.4855, 0.51625), (0.33599, 0.33863), (0.6450, 0.6626), and (0.402645, 0.403030), respectively. This information supplies the reason for the limitation of the useful range of the relative frequency spectrum. Because of the extreme nonlinearity of pulse-frequency modulation, we cannot deduce the behavior of the general periodic signal from the behavior of its sinusoidal components, but we have to apply methods described in this paper directly to the particular wave form studied. This is illustrated by the example in the Appendix.