Modulation Methods Related to Sine-Wave Crossings

A bounded band-limited signal may be represented by its sine-wave crossings, i.e., by a set of points on the time axis at which it crosses a reference sinusoid. If, at these points, pulses of a standard shape are generated, we obtain a position modulated pulse train. This pulse train is analyzed in detail. Two other modulation methods related to sine-wave crossings are also discussed, namely, edge position modulation of a square wave and bipolar pulse duration modulation. In all cases, the modulated waves may be expressed as sums of an infinite number of sinusuidal carriers amplitude modulated by Chebyshev polynomials of modulating signals.