This paper is concerned with adaptive noise reduction based on the fast recursive least squares (FRLS) algorithm. It is well known that the fast recursive least squares (FRLS) algorithm suffers from numerical instability when operating under the effects of finite precision arithmetic. Several numerical solutions of stabilization were proposed in the case of stationary signals. In this work a new version of a numerically stable FRLS algorithm (NS-FRLS) is proposed. The stability characteristics of this new stabilized algorithm are analysed. The analysis is based on a linear model for the errors in the states of the adaptive filter. Experimental results confirm the merits of adaptive filtering with the NS-FRLS algorithm over optimum filtering using the solution provided by Wiener-Hopf equations.

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It is well known that the interleaver plays a critical role in the performance of turbo codes and its design using random and deterministic permutations. In this paper, we present a new method to design a deterministic interleaver with random-like behavior based on two-dimensional chaotic map, so called lozi map. The designed interleaver is called chaotic interleaver. The statistical properties and the performance of such interleaver have been investigated and compared with random interleaver and dithered golden interleaver. Chaotic interleaver results in lowering the latency and the complexity of implementation and enhance the reliability and the security of the communication system.

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We propose a modified version of the standard homomorphic method to design a minimum-phase inverse filter for non-minimum-phase impulse responses equalization. In the proposed approach some of the dominant poles of the filter transfer function are replaced by new ones before carrying out the inverse DFT. This method is useful when partial magnitude equalization is intended. Results for an impulse response measured in the car interior show that by using the modified version we can control the sound quality more precisely than when using the standard method.

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