An audio processing device, e.g. a hearing aid, comprising • at least one input unit (M; M1, M2; IU 1,..., IU M) for providing a time-frequency representation Y(k,n) of an electric input signal representing a time variant sound signal consisting of target speech signal components S(k,n) from a target sound source TS and noise signal components N(k,n) from other sources than the target sound source, where k and n are frequency band and time frame indices, respectively, • an SNR estimation system configured to ∘ determine a first signal to noise ratio SNR estimate γ(k,n) of said electric input signal, and to ∘ determine a second target signal to noise ratio SNR estimate ζ(k,n) by smoothing said first signal to noise ratio estimate γ(k,n) based on a recursive algorithm, said smoothing being implemented as a low pass filter with an adaptive time constant or low-pass cut-off frequency determined in dependence of the first and/or the second signal to noise ratio estimates, and characterized in that the adaptive time constant or low-pass cut-off frequency of the low pass filter for a given frequency index k is determined in dependence of the first and/or the second signal to noise ratio estimates corresponding to a number of frequency indices k' including the frequency index k. • at least one input unit (M; M1, M2; IU 1,..., IU M) for providing a time-frequency representation Y(k,n) of an electric input signal representing a time variant sound signal consisting of target speech signal components S(k,n) from a target sound source TS and noise signal components N(k,n) from other sources than the target sound source, where k and n are frequency band and time frame indices, respectively, • an SNR estimation system configured to ∘ determine a first signal to noise ratio SNR estimate γ(k,n) of said electric input signal, and to ∘ determine a second target signal to noise ratio SNR estimate ζ(k,n) by smoothing said first signal to noise ratio estimate γ(k,n) based on a recursive algorithm, said smoothing being implemented as a low pass filter with an adaptive time constant or low-pass cut-off frequency determined in dependence of the first and/or the second signal to noise ratio estimates, and characterized in that the adaptive time constant or low-pass cut-off frequency of the low pass filter for a given frequency index k is determined in dependence of the first and/or the second signal to noise ratio estimates corresponding to a number of frequency indices k' including the frequency index k. ∘ determine a first signal to noise ratio SNR estimate γ(k,n) of said electric input signal, and to ∘ determine a second target signal to noise ratio SNR estimate ζ(k,n) by smoothing said first signal to noise ratio estimate γ(k,n) based on a recursive algorithm, said smoothing being implemented as a low pass filter with an adaptive time constant or low-pass cut-off frequency determined in dependence of the first and/or the second signal to noise ratio estimates, and characterized in that the adaptive time constant or low-pass cut-off frequency of the low pass filter for a given frequency index k is determined in dependence of the first and/or the second signal to noise ratio estimates corresponding to a number of frequency indices k' including the frequency index k.