Spectra for a class of asynchronous FM waves

The spectral density of a frequency modulated carrier is evaluated for the case when the modulating baseband wave is a “quantized” random facsimile signal. By this nonsynchronous form of modulation we mean holding one of the allowed set of transmitted frequencies for a finite, but randomly distributed, time before switching to another frequency while maintaining phase continuity. Emphasis is given to the Poisson case of exponentially distributed intervals between transitions, and some typical curves for discrete level and continuous level situations are included.