Random Pulse Train Spectrum Calculation Unleashed

TL;DR

This paper presents a comprehensive solution for calculating the power spectrum density of random pulse trains, correcting past misconceptions and extending the theory to various pulse train types with validated simulations.

Contribution

It provides the first complete solution for the spectrum calculation of random pulse trains, including cases with discrete spectra and unbalanced symbol durations.

Findings

Spectrum peaks are present in the analyzed pulse trains.

Theoretical results are validated through simulations.

Characteristics of spectrum peaks are thoroughly investigated.

Abstract

For the first time the problem of the full solution for the calculation of the power spectrum density of the random pulse train is solved. This well known problem led to a mistaken publication in the past and even its partial solution was considered worthy of publication in a textbook. The little known solution for only the continues random pulse train spectrum is explained by examples and is extended to cover each signal having a discrete spectrum, too. A developed approach is used to derive the general equation for two important representative pulse trains with unbalanced symbol duration: a signal with stretched pulse with a transition from one to zero, and shortened blank symbols. The developed theoretical results are validated by simulation. It is shown that the pulse trains under consideration pose spectrum peaks. The characteristics of these peaks are investigated.