Conventional electric field mill designs are not able to measure quasi-static atmospheric electric fields in the vicinity of high-voltage power systems. The electric fields generated by such power systems produce severe perturbations to the quasi-static background electric field. Filtering of these perturbations by the field mill circuitry seems to be easy because of their periodically alternating character. However, the operation of a field mill involves an effective signal filtering method, as presented in this paper. Because field mill operation gives rise to amplitude modulation of the incident electric field under measurement, a new technique based on coherent demodulation and notch filtering is proposed. Simulation and experimental results validate the excellent performance of the proposed method for measuring sudden step functions in electric field in presence of a severely perturbed ambient.