Exact spectral evaluation of the family of digital pulse interval modulated signals

This paper presents a closed-form spectral evaluation of the family of digital pulse interval modulation (DPIM) schemes, where the information is contained in the relative distance between successive pulses. The framework for spectral evaluation is that of stationary symbol sequences derived from variable-length word sequences, which considers the issue of stationarization, a preliminary task to spectral analysis. For all the considered modulation schemes, the spectrum turns out to be a rational function of exp(j2πfT), where T is the slot duration. Moreover, spectral lines occur at integer multiples of 1/T, but occasionally may also occur at submultiples of 1/T