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本文详细讨论了自适应滤波器的阶数（LMS算法中为加权数目）与输入信号相关性和稳态均方误差的关系。通过公式推导，从理论上证明了增加阶数并不能保证减小稳态均方误差。对于具体的输入信号，存在一个最佳（或准最佳）的阶数，使稳态均方误差最小，再增阶数，稳态均方误差有增大的可能。作者以强相关的直流信号和弱相关的正弦信号分别作为自适应滤波器的输入信号进行了计算机仿真实验，实验结果与公式推导结果一致。该理论为自适应滤波器设计时阶数的选择提供了理论指导，有实际意义。
This paper discusses in detail the dependence of the adaptive filter order (weighted number in the LMS algorithm) on the input signal and the steady-state mean-square error. Through formula derivation, it is theoretically proved that increasing the order does not guarantee to reduce the steady state mean square error. For the specific input signal, there is an optimal (or quasi-optimal) order, so that the steady-state mean square error minimum, then the number of orders, the steady-state mean square error may increase. The author uses the strong correlation DC signal and the weakly correlated sine signal as the input signals of the adaptive filter respectively to carry on the computer simulation experiment. The experimental results are consistent with the formulas. The theory provides a theoretical guide for the choice of adaptive filter design order, and has practical significance.