Synthesis of two second-order discrete time-varying filters (DTVF), capable of suppressing a sine signal with arbitrary frequency variation, is given. These structures are obtained by using the time-warping concept. Noise analysis is carried out for these two DTVF's and their performance compared. It is shown that for the particular application considered in this paper, the rule of time-dependence of the DTVF (the synchronization), may be effectively obtained by using a phase-locked loop (PIX) system. As an example, the DTVF + PLL system is used for synchronous phase estimation of a sine wave corrupted by a closely spaced FM interference. Simulation results are provided to substantiate the analysis as well as reveal the efficiency of the proposed time-varying system.