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.