Audio signal processing for adaptive de-reverberation uses a least mean squares (LMS) filter that has improved convergence over conventional LMS filters, making embodiments practical for reducing the effects of reverberation for use in many portable and embedded devices, such as smartphones, tablets, laptops, and hearing aids, for applications such as speech recognition and audio communication in general. The LMS filter employs a frequency-dependent adaptive step size to speed up the convergence of the predictive filter process, requiring fewer computational steps compared to a conventional LMS filter applied to the same inputs. The improved convergence is achieved at low memory consumption cost. Controlling the updates of the prediction filter in a high non-stationary condition of the acoustic channel improves the performance under such conditions. The techniques are suitable for single or multiple channels and are applicable to microphone array processing.