Spectral Density Bounds on an FM Wave

Upper and lower bounds on the spectral density of a sinusoidal carrier frequency modulated by a band-limited Gaussian noise signal are derived and we show that these bounds are very close to each other if the ratio of the rms frequency deviation to the maximum modulating frequency is even moderately high. We then show that the results obtained from the quasi-static approximation, often used in such cases, are too small for large and that this low-frequency approximation cannot be used in cases where the behavior on the tails is of importance.