The present invention relates to a multi-band noise reduction system for digital audio signals producing a noise reduced digital audio output signal from a digital audio signal. The digital audio signal comprises a target signal and a noise signal, i.e. a noisy digital audio signal. The multi-band noise reduction system operates on a plurality of sub-band signals derived from the digital audio signal and comprises a second or adaptive signal-to-noise ratio estimator which is configured for filtering a plurality of first signal-to-noise ratio estimates of the plurality of sub-band signals with respective time-varying low-pass filters to produce respective second signal-to-noise ratio estimates of the plurality of sub-band signals. A low-pass cut-off frequency of each of the time-varying low-pass filters is adaptable in accordance with a first signal-to-noise ratio estimate determined by a first signal-to-noise ratio estimator and/or the second signal-to-noise ratio estimate of the sub-band signal.