Power Spectrum of a Digital, Frequency-Modulation Signal

In recent years, digital-frequency and phase-modulation techniques have been increasingly important in radio, waveguide, and optical communication systems. An important parameter in the statistical description of a signal is its spectral density, which defines the average power density of the signal as a function of frequency. In addition to furnishing an estimate of bandwidth requirements, the knowledge of the spectral density is also essential in the evaluation of mutual interference between channels. In this paper, we extend the techniques developed in Ref. 1 for digital PSK to the case of digital FSK with phase-continuous transitions, such as may be obtained at the output of a voltage-controlled oscillator driven by a digital baseband wave. We assume that the sinusoidal carrier is 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. It is generally assumed that the symbols transmitted during different time slots are statistically independent and identically distributed. We express the spectral density of such an ensemble of continuousphase, constant-envelope, digital, FM waves as a compact Hermitian 1095