The device calculates a first frequency-dependent useful signal level estimator for the frame. The transfer function of a first noise-reducing filter is determined on the basis of the first useful signal level estimator and of a frequency-dependent noise level estimator. A second frequency-dependent useful signal level estimator for the frame is then calculated by combining the spectrum of the input signal and the transfer function of the first noise-reducing filter. The transfer function of a second noise-reducing filter is determined on the basis of the second useful signal level estimator and of the noise level estimator. The latter transfer function is used in a frame filtering operation to produce a signal with reduced noise.