变步长和变正则化因子的子带自适应滤波算法研究

子带自适应滤波算法技术由于复杂度低、收敛速度快而被广泛的应用。但是传统的子带自适应算法受到混叠分量的影响使得性能下降。申请者已经提出了一种新的子带自适应算法（improved multiband-structured subband adaptive filter,IMSAF），解决了这个难题。但是IMSAF算法在收敛速度和稳态失调之间存在折中，目前尚无针对这个问题的专门研究。本项目从不同的准则出发提出了变步长和变正则化因子的IMSAF算法，在算法的不同收敛阶段采用不用的步长或规则化因子，使得算法同时达到较快的收敛速度和较小的稳态失调，进一步对系数向量的迭代进行约束提出对外界干扰不敏感的变步长IMSAF算法。本研究对输入信号高度相关的场合例如回声抵消、有源噪声控制和啸叫抑制等具有重要的理论意义和实用价值。

Subband adaptive filtering algorithms are widely used due to its low complexity and fast convergence rate. However, the performance of the traditional subband adaptive filter is decreased because of the aliasing and band-edge effects. We have proposed an improved multiband-structured subband adaptive filter (IMSAF) to address this problem. But there is a trade-off between the convergence rate and the steady-state misalignment, which has not been studied in the literature. We plan to propose several variable step-size and variable regularization factor IMSAF algorithms based on different optimization criterions in this project. The proposed algorithms can achieve both fast convergence rate and low steady-state misalignment by using time-varying step-size or variable regularization factor. Moreover, a robust variable step-size IMSAF algorithm is presented subject to a constraint on the norm of the adaptive filter update. The proposed algorithms can be useful for many applications such as acoustic echo cancellation, active noise control and adaptive acoustic feedback suppression.