Synthesis of discrete time-varying null filters for frequency-varying signals using the time-warping technique

A synthesis of two second-order discrete time-varying filters (DTVF), capable of suppressing a sine signal with arbitrary frequency variation, is presented. These structures are obtained by using the time-warping concept. A noise analysis is carried out for these two DTVFs and their performance is compared. It is shown that for the particular application considered, the rule of time-dependence of the DTVF (the synchronization) may be effectively obtained by using a phase-locked loop (PLL) system. As an example, the DTVF-PLL system is used for synchronous phase estimation of a sine wave corrupted by closely spaced FM interference. Simulation results are provided to substantiate the analysis and demonstrate the efficiency of the proposed time-varying system. The main feature of the TLM method is its formulation and programming simplicity. The method also generates a large amount of information; not only is the impulse response of a structure obtained, yielding in turn its response to any excitation, but the characteristics of the dominant and higher order modes are also accessible in the frequency domain through the Fourier transform