This thesis deals with several open problems in acoustic echo cancellati on and acoustic feedback control. Our main goal has been to develop solu tions that provide a high performance and sound quality, and behave in a robust way in realistic conditions. This can be achieved by departing f rom the traditional ad-hoc methods, and instead deriving theoretically w ell-founded solutions, based on results from parameter estimation and sy stem identification. In the development of these solutions, the computat ional efficiency has permanently been taken into account as a design con straint, in that the complexity increase compared to the state-of-the-ar t solutions should not exceed 50 % of the original complexity. In the context of acoustic echo cancellation, we have investigated the p roblems of double-talk robustness, acoustic echo path undermodeling, and poor excitation. The two former problems have been tackled by including adaptive decorrelation filters in the adaptive filtering algorithm, wit h the aim of whitening the near-end signal component and the residual ec ho component resulting from undermodeling. These decorrelation filters c an be identified concurrently with the acoustic echo path by using the p rediction error method (PEM) for system identification. As a result, a 3 0-40 dB misadjustment improvement (in the double-talk case) and a 20-35 dB variance decrease (in the undermodeling case) have been obtained, at the cost of a complexity increase of 50 % compared to the normalize d least mean squares (NLMS) algorithm. The poor excitation problem has b een approached from a Bayesian minimum mean square error (MMSE) point of view. This approach has led to the use of a regularization matrix diffe rent from the traditional scaled identity matrix, which may incorporate prior knowledge on the acoustic echo path. It has moreover been shown th at the existing proportionate adaptation algorithms can be viewed as a s pecial case of the proposed approach to regularization. A misadjustment improvement up to 10 dB has been obtained with a regularized NLMS-type a lgorithm that requires only 25 % more computations than the origina l NLMS algorithm. Two approaches to acoustic feedback control have been considered in this thesis, namely notch-filter-based howling suppression (NHS) and adaptiv e feedback cancellation (AFC). In the context of NHS, we have developed a novel parametric frequency estimation method, which is characterized b y a computational complexity that is linear in the data record length. A lso, a new design procedure for biquadratic parametric equalizer filters is proposed, based on a technique known as pole-zero placement. In the context of AFC, the PEM-based AFC approach that was proposed earlier for hearing aid AFC has been generalized to room acoustic and audio applica tions. The PEM-based approach relies on the identification of a near-end signal model that can be used in the design of decorrelating prefilters . These prefilters are aimed at resolving the AFC closed-loop signal cor relation problem and hence providing an unbiased acoustic feedback path model. We have obtained a misadjustment improvement of 7 dB compared to the hearing aid PEM-based AFC algorithm and of 12 dB compared to the NLM S algorithm, at the cost of a 25-50 % complexity increase compared to NLMS. In a comparative evaluation with the state-of-the-art acoustic feedback control methods, the PEM-based AFC approach was shown to outper form the existing phase-modulating feedback control (PFC) and NHS method s, as well as the AFC methods that apply a decorrelation in the closed s ignal loop, in terms of the achievable maximum stable gain and sound qua lity, both for speech and audio signals.
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