A multi-band noise reduction system for digital audio signals, comprising: a signal input for receipt of a digital audio input signal comprising a target signal and a noise signal, an analysis filter bank configured for dividing the digital audio input signal into a plurality of sub-band signals Y k ( n), a noise estimator configured for determining respective sub-band noise estimates σ ^ k 2 n of the plurality of sub-band signals Y k ( n), a first signal-to-noise ratio estimator configured for determining respective first signal-to-noise ratio estimates ξ k 0 n of the plurality of sub-band signals based on the respective sub-band noise estimation signals and the respective sub-band signals Y k ( n), a second signal-to-noise ratio estimator configured for filtering the plurality of first signal-to-noise ratio estimates ξ k 0 n of the plurality of sub-band signals Y k ( n) with respective time-varying low-pass filters to produce respective second signal-to-noise ratio estimates ζ k ( n) of the plurality of sub-band signals Y k ( n) wherein a low-pass cut-off frequency of each of the time-varying low-pass filters is adaptable in accordance with the first signal-to-noise ratio estimate or the second signal-to- noise ratio estimate of the sub-band signal, a gain calculator configured for applying respective time-varying gains G k ( n) to the plurality of sub-band signals Y k ( n) based on the respective second signal-to-noise ratio estimates ζ k ( n) and respective sub-band gain laws to produce a plurality of noise compensated sub-band signals, a synthesis filter bank configured to combine the plurality of noise compensated sub-band signals into a noise reduced digital audio output signal Audio Out(t) at a signal output. a signal input for receipt of a digital audio input signal comprising a target signal and a noise signal, an analysis filter bank configured for dividing the digital audio input signal into a plurality of sub-band signals Y k ( n), a noise estimator configured for determining respective sub-band noise estimates σ ^ k 2 n of the plurality of sub-band signals Y k ( n), a first signal-to-noise ratio estimator configured for determining respective first signal-to-noise ratio estimates ξ k 0 n of the plurality of sub-band signals based on the respective sub-band noise estimation signals and the respective sub-band signals Y k ( n), a second signal-to-noise ratio estimator configured for filtering the plurality of first signal-to-noise ratio estimates ξ k 0 n of the plurality of sub-band signals Y k ( n) with respective time-varying low-pass filters to produce respective second signal-to-noise ratio estimates ζ k ( n) of the plurality of sub-band signals Y k ( n) wherein a low-pass cut-off frequency of each of the time-varying low-pass filters is adaptable in accordance with the first signal-to-noise ratio estimate or the second signal-to- noise ratio estimate of the sub-band signal, a gain calculator configured for applying respective time-varying gains G k ( n) to the plurality of sub-band signals Y k ( n) based on the respective second signal-to-noise ratio estimates ζ k ( n) and respective sub-band gain laws to produce a plurality of noise compensated sub-band signals, a synthesis filter bank configured to combine the plurality of noise compensated sub-band signals into a noise reduced digital audio output signal Audio Out(t) at a signal output.