A device for decoding audio signals subjected to a noise-reduction encoding such as a Dolby-B encoding comprises a plurality of processing blocks (612, 616, 620, 624, 628, 632, 636, 640) for generating, starting from an input signal (610) containing the audio signal subjected to encoding superimposed on a noise component, an output signal (626) consisting of a replication of the audio signal with the noise component reduced. The aforesaid processing blocks are implemented in a digital form and comprise a sliding-band filtering structure (612) fed with the input signal (610) and designed to generate a filtered signal (614). The filtered signal (614) is fed, according to a general feedforward scheme, to an overshoot-suppression stage (616) in view of the generation, in an adder node (620), of a difference signal (622) starting from which the output signal is obtained via filtering (624). The same filtered signal (614) is also used to drive a control chain (632, 636, 640) preceded by a further linear filter (628). The control chain generates respective control signals for the sliding-band filtering structure (612) and for the filters (624, 628) that reproduce the output signal (626) and the input signal (630) for the control chain. The aforesaid two filters (624, 628) are preferably all-pole filters, the function of which is to minimize the error introduced by the sliding-band filtering structure (612).