Linear-harmonic generation

A linear-harmonic generator is a nonlinear device in which an applied cosine wave of amplitude A causes some harmonic(s) of the input to be generated with amplitude(s) proportional to A. Such devices find application in phase-envelope processing in some types of modulation and speech-transmission systems. The present paper provides a theoretical study of the ability some characteristics have to generate linear harmonics. Linear-harmonic generation by single-valued characteristics which are representable by piecewise linearisation and those representable by a power series are investigated. It is shown that piecewise linear characteristics cannot generate linearly odd components. Also, it is shown that a characteristic expanded by a power series cannot generate linear harmonics, for either even or odd components. A particular single-valued characteristic, which precisely generates odd-harmonic components, is found, although it cannot be practically realised without approximation.