Subband Kalman filtering for speech enhancement

Kalman filtering is an effective speech-enhancement technique, in which speech signals are usually modeled as autoregressive (AR) processes and represented in the state-space domain. Since AR coefficients identification and Kalman filtering require extensive computations, real-time implementation of this approach is difficult. This paper proposes a simple and practical scheme that overcomes these obstacles. Speech signals are first decomposed into subbands. Subband speech signals are then modeled as low-order AR processes, such that low-order Kalman filters can be applied. Enhanced fullband speech signals are finally obtained by combining the enhanced subband speech signals. To identify AR coefficients, prediction-error filters adapted by the LMS algorithm are applied. Due to noisy inputs, the LMS algorithm converges to biased solutions. The performance of the Kalman filter with biased parameters is analyzed. It is shown that accurate estimates of AR coefficients are not required when the driving-noise variance is properly estimated. New methods for making such estimates are proposed. Thus, we can tolerate biased AR coefficients and take advantage of the LMS algorithm's simple structure. Simulation results show that speech enhancement in the subband domain not only greatly reduces the computational complexity, but also achieves better performance compared to that in the fullband domain.