The generalized leaky filtered–x least mean square (GLFxLMS) algorithm can reduce the noise amplification caused by the waterbed effect in feedback active control systems effectively; however, it suffers from a high computation complexity. Hence, a frequency band constrained filtered–x least mean square algorithm is proposed to reduce the computation complexity of the GLFxLMS algorithm by replacing the penalty term containing a symmetric Toeplitz matrix in the cost function with the mean square of a penalty signal. The simulation results based on the measured transfer functions of an active headrest system show that the proposed algorithm has the same performance as the GLFxLMS algorithm, but with much lower computation complexity.

中文翻译：

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反馈有源控制系统的频带约束滤波x最小均方算法

广义的泄漏滤波-x最小均方（GLFxLMS）算法可以有效减少反馈主动控制系统中水床效应引起的噪声放大。但是，它具有很高的计算复杂度。因此，提出了一种频带受限的滤波-x最小均方算法，通过用代价信号的均方值代替代价函数中包含对称Toeplitz矩阵的惩罚项来降低GLFxLMS算法的计算复杂度。基于主动式头枕系统的传递函数的仿真结果表明，该算法与GLFxLMS算法具有相同的性能，但计算复杂度低得多。