The zero-crossing phase-lock loop: Results from discrete dynamical theory (Q5938948)

The authors deals with some aspects of the discrete map (1) \(\psi_n= \psi_{n-1}- \kappa\sin \psi_{n-1}\), where \(\kappa\in [0,4.6033]\). For this range of \(\kappa\), \(\psi\) maps the interval \((-\pi,\pi)\) into itself and \(\psi\) derives from an important component of digital communication receivers: it represents the response of a first order zero-crossing discrete phase-lock loop (ZC-DPLL) to an unmodulated carrier with a phase offset. Dynamical systems theory immediately provides a more complete picture of ZC-DPLL operation. The authors also find that the ZC-DPLL displays unusual features derived from its odd symmetry and bimodality.