Spectral Density Bounds of a PM Wave
V.K. Prabhu, Harrison E. Rowe · Bell System Technical Journal · 1969
In this paper we derive upper and lower bounds of the spectrum of a sinusoidal carrier phase modulated by gaussian noise having a rectangular power spectrum. It has been found in practice that such a random process adequately simulates for some purposes, a frequency division multiplex signal, a composite speech signal, and so on. We show that these upper and lower bounds of the spectrum are very close to each other if the root mean square phase deviation of the carrier is even moderately high. Also, a simple method called the saddle-point method can be used at all frequencies f to estimate the spectrum with less than ten percent error. We also show that the results obtained from the quasistatic approximation, often used in such cases, are too small for large f, and that this low-frequency approximation cannot be used in cases where the behavior on the tails is of importance.