On the Differential Equation for the Generation of Frequency Modulation

Representations are presented for the general solution of thelinear differential equation associated with the electronicgeneration of frequency modulated signals. The frequency modulationcomponent is determined explicitly by an orthogonal fundamentalsolution matrix, while the amplitude modulation component, whicharises as an impurity in the generation process, is discussedwith the aid of elementary aspects of the theory of Lie algebras.The Lie algebra thus defined is three dimensional and algebraicallysimple. Asymptotic representations of the amplitude modulationcomponent to the first-order in the absolute frequency deviationare shown to be completely prescribed by the basis vectors chosenfor the Lie algebra.