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In this paper, we propose the modulation-domain Kalman filter (MDKF) for speech enhancement. In contrast to previous modulation domain-enhancement methods based on 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 modulation phase tends to contain more speech information than acoustic phase. Experimental results from the NOIZEUS corpus show the ideal MDKF (with clean speech parameters) to outperform all the acoustic and time-domain enhancement methods that were evaluated, including the conventional 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.