In this paper, the problem of extracting periodic signals, like voiced speech or tones in music, from noisy observations or mixtures of periodic signals is considered, and, in particular, the problem of designing filters for such a task. We propose a novel filter design that 1) is specifically aimed at extracting periodic signals, 2) is optimal given the observed signal and thus signal-adaptive, and 3) offers a full parametrization of the periodic signal. The found filters can be used for a multitude of applications including signal compression, parameter estimation, enhancement, and separation. Some illustrative signal examples demonstrate its superior properties as compared to other similar filters.