Abstract: The high requirements of digital mobile radiotelephone communication under the GSM Standard with respect to synchronization of a mobile radiotelephone to a fixed radiotelephone station is performed by frequently (four times per so-called baseband frequency cycle) sampling contemporary in-phase and quadrature phase components of received GMSK digital signals and utilization of time slots respectively containing a frequency correction burst, a normal burst and an extended synchronization burst, respectively for initial synchronization, normal maintenance of synchronization during communication and a background procedure during normal operation. The decoding of the GMSK signal provides one-bit of information from each pair of in-phase and quadrature components sampled. The sampling of in-phase and quadrature components greatly simplifies the synchronizing procedure.