Kalman filter analysis for quasi-periodic signals

An Optimal lter for extracting quasi-periodic signals such as a voiced speech or instrumental sound from the noise-corrupted observation are proposed. They are derived through the Kalman-Bucy lter analysis in which the dynamics of amplitude and pitch uctuations are described through Itô stochastic di erential equations. The Laplace analysis to the lter equation leads to three types of comb lters, i.e., constant-BW (-bandwidth) type, constant-Q type and those mixture type that have robustness to the amplitude uctuation, pitch uctuation and both of them, respectively. All-pole digital lters can be also realized for real-time processing. Examples of lter design are presented, and the performance of harmonics extraction is examined by comparison between the constant-BW type and constant-Q type.