Power Spectrum of a Digital, Frequency-Modulation Signal

We present the power spectrum of a sinusoidal carrier, frequency modulated by a random baseband pulse train in which the signaling-pulse duration is finite and the signal pulses may overlap and have different shapes. Symbols transmitted during different time slots are assumed to be statistically independent and identically distributed. The spectral density appears as a Hermitian form suitable for numerical computation by a digital computer. Simple conditions in terms of the modulation parameters are given under which discrete spectral lines are present in the spectrum. Several examples are given to illustrate the method.