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本文推导出实数LMS算法自适应线谱增强器稳态响应的闭式解。推导首先对输入线谱信号的协方差矩阵作正交分解,再运用Woodbury引理对矩阵求逆并直接得到最佳权向量的解。通过传统的离散付氏变换又求得了系统的最佳传递函数。本文给出了最佳传递函数的计算机仿真曲线以证明理论分析的正确性。
In this paper, the closed-form solution to the steady-state response of the adaptive line-spectrum enhancer of real LMS algorithm is deduced. The derivation is based on the orthogonal decomposition of the covariance matrix of the input line spectral signal, and then using Woodbury’s Lemma to invert the matrix and obtain the solution of the optimal weight vector directly. Through the traditional discrete Fourier transform, we obtain the optimal transfer function of the system. This paper gives the computer simulation curve of the best transfer function to prove the correctness of the theoretical analysis.