Modulation-domain Kalman filtering for single-channel speech enhancement

In this paper, we investigate the modulation-domain Kalman filter (MDKF) and compare its performance with other time-domain and acoustic-domain speech enhancement methods. In contrast to previously reported modulation domain-enhancement methods based on fixed bandpass filtering, the MDKF is an adaptive and linear MMSE estimator that uses models of the temporal changes of the magnitude spectrum for both speech and noise. Also, because the Kalman filter is a joint magnitude and phase spectrum estimator, under non-stationarity assumptions, it is highly suited for modulation-domain processing, as phase information has been shown to play an important role in the modulation domain. We have found that the Kalman filter is better suited for processing in the modulation-domain, rather than in the time-domain, since the low order linear predictor is sufficient at modelling the dynamics of slow changes in the modulation domain, while being insufficient at modelling the long-term correlation speech information in the time domain. As a result, the MDKF method produces enhanced speech that has very minimal distortion and residual noise, in the ideal case. The results from objective experiments and blind subjective listening tests using the NOIZEUS corpus show that the MDKF (with clean speech parameters) outperforms all the acoustic and time-domain enhancement methods that were evaluated, including the time-domain Kalman filter with clean speech parameters. A practical MDKF that uses the MMSE-STSA method to enhance noisy speech in the acoustic domain prior to LPC analysis was also evaluated and showed promising results.