Kalman filter analysis for quasi-periodic signals

An optimal filter for extracting quasi-periodic signals such as voiced speech or instrumental sound from noise-corrupted observation are proposed. They are derived through the Kalman-Bucy filter analysis in which the dynamics of amplitude and pitch fluctuations are described through Ito stochastic differential equations. The Laplace analysis of the filter equation leads to three types of comb filters, ie, constant-BW (-bandwidth) type, constant-Q type and a mixture type that has robustness to the amplitude fluctuation, pitch fluctuation and both these, respectively. All-pole digital filters can be also realized for real-time processing. Examples of filter design are presented, and the performance of harmonics extraction is examined by comparison between the constant-BW type and constant-Q type