Spectral Density Bounds of a PM Wave

It has been found in practice that a bandlimited random gaussian noise having a rectangular power spectrum adequately simulates for some purposes a wideband composite speech signal, a frequency division multiplex baseband signal consisting of a group of single sideband carrier telephone channels, and so on.1 In the design of communication systems, the spectral characteristics of a sinusoidal carrier phase modulated by such a baseband signal are of great interest; various methods have been used in recent years to estimate this spectrum for large and small values of mean square phase deviation of the wave, both close to and far from the carrier frequency (that is, in the principal part of the spectrum and far down on the tails of the spectrum respectively) . 1-8 It has been shown that the spectrum may be expanded as an infinite series of weighted convolution terms.2,5,7,8 This series may be used to estimate the principal part of the spectrum (close to the 769 770 T H E BELL SYSTEM TECHNICAL JOURNAL, MARCH