Abstract-Hands-free devices are often used in a noisy and reverberant environment. Therefore, the received microphone signal does not only contain the desired near-end speech signal but also interferences such as room reverberation that is caused by the near-end source, background noise and a far-end echo signal that results from the acoustic coupling between the loudspeaker and the microphone. These interferences degrade the fidelity and intelligibility of near-end speech. In the last two decades, postfilters have been developed that can be used in conjunction with a single microphone acoustic echo canceller to enhance the near-end speech. In previous works, spectral enhancement techniques have been used to suppress residual echo and background noise for single microphone acoustic echo cancellers. However, dereverberation of the near-end speech was not addressed in this context. Recently, practically feasible spectral enhancement techniques to suppress reverberation have emerged. In this paper, we derive a novel spectral variance estimator for the late reverberation of the near-end speech. Residual echo will be present at the output of the acoustic echo canceller when the acoustic echo path cannot be completely modeled by the adaptive filter. A spectral variance estimator for the so-called late residual echo that results from the deficient length of the adaptive filter is derived. Both estimators are based on a statistical reverberation model. The model parameters depend on the reverberation time of the room, which can be obtained using the estimated acoustic echo path. A novel postfilter is developed which suppresses late reverberation of the near-end speech, residual echo and background noise, and maintains a constant residual background noise level. Experimental results demonstrate the beneficial use of the developed system for reducing reverberation, residual echo, and background noise. S. Gannot is with the School of Engineering, Bar-Ilan University, Ramat-Gan 52900, Israel (e-mail: gannot@eng.biu.ac.il).I. Cohen is with the Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel (e-mail: icohen@ee.technion.ac.il). P. C. W. Sommen is with the Signal Processing

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. (1987). Convergence analysis of a frequency-domain adaptive filter with exponential power averaging and generalized window function. IEEE Transactions on Circuits and Systems, 34(7), 788-798. DOI: 10.1109/TCS.1987 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract-One of the advantages of a Frequency-Domain Adaptive Filter (FDAF') is that one can achieve convergence at a constant rate over the whole frequency range by choosing the adaptation constant for each frequency bin I equal to the overall adaptation constant divided by an estimate of the input power at this frequency bin. A commonly used method, applied in this paper, to estimate the input power is to do an exponentially weighting with smoothing constant B on the magnitude squared of the input values at each frequency bin 1. Furthermore, it is known that a correctly imfdemented FDAF, using the overlapsave method, contains five 2 N-points Fast Fourier Transforms (FFT). Two of these are used to force the last N points of the time-domain augmented impulse response to zero by applying a particular window function. In this paper, an analysis is given of the'FDAF where the window function is generalized. Using these results, the convergence behavior of FDAF's with various window functions is compared. Furthermore, the analysis describes the influence of /3 on the convergence behavior of the FDAF over the whole convergence range.

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