Distortion Produced in a Noise Modulated FM Signal by Nonlinear Attenuation and Phase Shift

An expression is given for the FM distortion introduced by a transducer whose attenuation and phase shift depend upon the frequency in an arbitrary way. This expression appears to be difficult to evaluate, but it yields useful approximations for the second and third order modulation terms. In all of the work, it is assumed that the distortion is small compared to the signal, and that the signal can be represented by a random noise having the same power spectrum. INTKODUCTION A number of workers have been concerned with the problem of computing the distortion introduced by a transducer when an FM wave passes through it. Some of the earliest results were published by Carson and Fry 1 and by van der Pol." Several contributions to the subject have been made recently in connection with studies of microwave radio systems. An excellent paper on this subject has been published recently by R. G. Medhurst and G. F. Small.3 Although their results differ considerably in form from those given here, they are nevertheless closely related to ours -- their "sinusoidal variations of transmission characteristics" being special cases of our "nonlinear attenuation and phase shift." Here we treat the problem by applying a method used in a recent paper4 to study the distortion produced by an echo. Two assumptions are made, (1) that the distortion is small compared to the signal, and (2) that the signal can be represented by a random noise which has the same power spectrum as the signal. In Section I, we review some known results and put them in a form suited to our needs.