This paper proposes to combine the multipurpose digital filter (MDF) and the discrete Fourier transform (DFT) for the transmission lines impedance estimation under fault conditions. The digital filtering requirements in protecting relays are critical, because it is relevant to attain precise, fast, and reliable line impedance estimation from faulted current and voltage signals. In this paper, the proposed filter removes the exponentially decaying DC offset from the current signal, enhancing the impedance estimation under transient conditions, and reducing the time of estimation. Comparisons are made respect to the DFT with a one-cycle rectangular window. Simulations are carried out in order to assess the proposal.Index Terms--Digital filtering, exponential decaying, impedance estimation, phasor estimation, filtering, protective functions.I.