New bound for the spectrum of an f.m. wave

Cheby¿shev and 4th-moment generalised Cheby¿shev bounds on the power in the tail of the spectrum of an f.m. wave have been known for several years. Here it is shown that, when the modulation is Gaussian with r.m.s. frequency deviation D and contains no modulating frequency higher than F, the fraction of the total power lying in frequencies exceeding that of the carrier by more than ¿>0 must be less than (¿eD2/F¿)¿/F. This bound is of the Chernoff type, being based on a suitably chosen value of the `moment-generating function¿ of the f.m. spectrum, which is obtained directly from the autocorrelation function of the f.m. wave. The bound falls off with increasing ¿ much faster than the previous bounds. Although it cannot be expected to be a good approximation to the power in the spectral tail, its simple form makes it convenient for such applications as the study of neighbouring-channel interference.