Room equalization has become essential for sound reproduction systems to provide the listener with the desired acoustical sensation. Recently, adaptive filters have been proposed as an effective tool in the core of these systems. In this context, this paper introduces different novel schemes based on the combination of adaptive filters idea: a versatile and flexible approach that permits obtaining adaptive schemes combining the capabilities of several independent adaptive filters. In this way, we have investigated the advantages of a scheme called combination of block-based adaptive filters which allows a blockwise combination splitting the adaptive filters into nonoverlapping blocks. This idea was previously applied to the plant identification problem, but has to be properly modified to obtain a suitable behavior in the equalization application. Moreover, we propose a scheme with the aim of further improving the equalization performance using the a priori knowledge of the energy distribution of the optimal inverse filter, where the block filters are chosen to fit with the coefficients energy distribution. Furthermore, the biased block-based filter is also introduced as a particular case of the combination scheme, especially suited for low signal-to-noise ratios (SNRs) or sparse scenarios. Although the combined schemes can be employed with any kind of adaptive filter, we employ the filtered-x improved proportionate normalized least mean square algorithm as basis of the proposed algorithms, allowing to introduce a novel combination scheme based on partitioned block schemes where different blocks of the adaptive filter use different parameter settings. Several experiments are included to evaluate the proposed algorithms in terms of convergence speed and steady-state behavior for different degrees of sparseness and SNRs.

This paper provides an analysis of the steady-state behavior of two biased adaptive algorithms recently introduced for listening room compensation, the biased filtered-x normalized least mean squares (Fx-BNLMS) and the biased filtered-x improved proportionate NLMS (Fx-BIPNLMS). We give theoretical results that show that the biased algorithms can outperform the unbiased ones in terms of the mean square error, especially in low signal-to-noise ratio (SNR) scenarios. Moreover, for impulse responses exhibiting high sparse-ness, the improved proportionate algorithms achieve faster convergence than the standard NLMS. Thereby, the advantages of the Fx-BIPNLMS algorithm are justified theoretically in terms of the excess mean square error. Simulation results show that there is a relatively good match between theory and practice, especially for low μ values.

Multichannel adaptive affine projection algorithms (multichannel AP) are currently under development for multichannel audio applications, mainly for transaural audio reproduction. These algorithms present several advantages for real time systems such as moderate computational cost, good stability, and adjustable convergence speed. However the basic version of the AP algorithm needs to be optimized to be used on digital signal processors working on real time. Thus several variants of AP and its fast version (FAP) have been developed. Regarding its computational cost and real time implementation, an N /spl times/ N inverse matrix have to be calculated in each algorithm iteration, being N the affine projection order. This paper presents a comparison between several versions of the AP algorithm for real time multichannel audio and proposes a series of recommendations, such as the initialization parameters, to use the variants of the AP algorithm in multichannel sound.