Using the parameters provided by the project Telesat LEO, this thesis addresses the Doppler frequency shift encountered when an earth terminal station receives signals from a LEO satellite. To achieve fast frequency synchronization, there is a necessity to construct a Costas loop to speed up the acquisition time. Based on the theoretical foundations of the PLL, this thesis reviews the theory of BPSK and QPSK Costas loops. Then the thesis creates a new way of achieving fast synchronization for a BPSK Costas loop by adding a quadri-correlator. An optimized way is then introduced, which guarantees both stability and rapidity of acquisition. The construction of a QPSK Costas loop is different from that of BPSK. The thesis then shows that the addition of a quadri-correlator cannot be used in a QPSK Costas loop, but that the synchronization time can still be reduced by changing the parameters in the loop filter.