SUMMARYAn optimum filter is designed for separating quasiperiodic signals (those with amplitude and period changing randomly but a rough periodicity kept) in a noisy environment. In the first half of the paper, a Wiener filter is derived with steadiness assumed in the variations of the amplitude and fundamental frequency. It is shown that the frequency characteristics are (1) comb characteristics of a constant BW (bandwidth) type if only the amplitude variations are taken into consideration, (2) comb characteristics of a constant Q type if only the variations of the fundamental frequency are taken into account, and (3) comb characteristics transitional from a constant BW type to a constant Q type as the harmonic changes from a lower order to a higher order when both are taken into account. In the latter half of the paper, a Kalman filter analysis is carried out for the case in which the statistical nature of the amplitude/fundamental frequency variations is time-varying. The random nature of the complex phase term is treated as state-dependent noise. By describing the signal model in terms of the Ito probability differential equation, the Kalman filter equation for the use of this model as a state space model is solved. In particular, it is shown by approximate solution that the center frequency and occupancy bandwidth of each narrowband filter are determined to follow the variations of the amplitude and fundamental frequency.