The performance of automatic speech recognition for signals acquired through a hands-free speech interface is limited by the adverse effect of the noise and the reverberation. Frequency domain blind signal processing techniques, like blind signal separation, have been used with success for suppressing the noise in real situation but they usually do not take into account the reverberation. In this paper, we present a method based on frequency domain blind signal extraction that is aimed at suppressing both the adverse effect of the noise and the reverberation.