LXXI. The distribution of energy in randomly modulated waves

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Abstract
The distribution of energy in high-frequency oscillations which are modulated by stationary, random disturbances such as shot and thermal noise is here examined in a number of important practical situations. In (a) the theory for frequency- and phase-modulation by normal random noise is developed in particular, as a model for speech-modulated carriers. The effect of spectral shape of the modulating noise on the intensity distribution of the modulated carrier is considered, and it is found that the lowest-frequency components of the modulation are most significant in this respect. For example, in frequency-modulation the carrier term is entirely absent when the modulating noise has a finite spectral density at and near zero-frequency, while in phase-modulation by the same disturbance the carrier component may contain a noticeable fraction of the modulated wave's energy. Particular attention is also given to the limiting cases of very slow frequency deviation, and it is found that such adiabatic sweeps spread the original spectrum. Part (b) contains a parallel discussion for the amplitude-modulation by normal random noise, including the effects of possible over-modulation.

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