Frequency-domain adaptation of causal digital filters
Frequency-domain adaptation of causal digital filters
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DOI：
10.1109/78.839982
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发表时间：
2000-05
期刊：
影响因子：
--
通讯作者：
S. Elliott;B. Rafaely
中科院分区：
文献类型：
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作者：
S. Elliott;B. Rafaely
因果FIR数字滤波器在离散频域中的适应被认为是，它示出了如何bin归一化形式的LMS算法可以收敛到一个有偏的解决方案，如线性预测的问题。牛顿算法的离散频域版本的推导，它是如何证明这可以收敛到最佳的因果解，即使是线性预测问题。该算法采用的参考信号的估计功率谱密度的频谱分解，其中完全非因果关系的一部分是使用之前的因果关系约束的自适应算法，和完全因果关系的一部分后应用的因果关系约束。谱因子可以从功率谱密度的递归估计在线计算，而不会损失太大的收敛速度。还描述了前馈控制器的自适应算法的扩展，在这种情况下，需要由工厂响应滤波的参考信号的频谱因子，并且这些示出为等于参考信号的频谱因子乘以最小相位部分或工厂频率响应。
The adaptation of causal FIR digital filters in the discrete frequency domain is considered, and it is shown how the bin-normalized form of the LMS algorithm can converge to a biased solution for problems such as linear prediction. A discrete frequency-domain version of Newton's algorithm is derived, and it is demonstrated how this can converge to the optimal causal solution, even for linear prediction problems. The algorithm employs a spectral factorization of the estimated power spectral density of the reference signal, the entirely noncausal part of which is used before the causality constraint in the adaptation algorithm, and the entirely causal part is applied after the causality constraint. The spectral factors can be calculated online from a recursive estimate of the power spectral density without too great a loss of convergence speed. The extension of the algorithm to the adaptation of feedforward controllers is also described, in which case, the spectral factors of the reference signals filtered by the plant response are required, and these are shown to be equal to the spectral factors of the reference signal multiplied by the minimum phase part or the plant frequency response.