Spectral density function of multilevel continuous-phase FM

Compact formulas are derived for the spectral density function of an ensemble of continuous-phase constant-envelope multilevel FM waves. The results are general and are presented in terms of averages of elementary functions. Both continuous and discrete spectra are treated, and conditions in terms of the modulation parameters are given under which lines in the spectrum are present. The formulas are applicable in the study ofN-ary FM data transmission systems as well as in pulse frequency modulation.