An optimal design of the extrapolated impulse response filter with analytical solutions
An optimal design of the extrapolated impulse response filter with analytical solutions
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DOI：
10.1016/j.sigpro.2011.12.026
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
Hao Wang;Li Zhao;Haixian Wang;S. Fang;Pingxiang Liu;Xuanmin Du
中科院分区：
文献类型：
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作者：
Hao Wang;Li Zhao;Haixian Wang;S. Fang;Pingxiang Liu;Xuanmin Du
基于主成分分析的外推脉冲响应滤波器设计通常比传统的非最优型滤波器设计性能更好。然而，在EIR设计中没有提出最优性。在本文中，EIR技术的线性表示的角度来理解。在此基础上，提出了一种EIR滤波器的设计方法。所提出的设计是最佳的最佳线性表示意义上的序列域。我们提出的设计的解决方案集理论推导。在解集内，解析地获得具有次最低系数灵敏度（CS）的解。如果使用我们提出的技术计算比例因子，则可以证明基于PCA的EIR滤波器（PCA-EIR）的设计是解决方案集内的解决方案。仿真实验验证了我们提出的EIR技术。我们提出的EIR技术执行以及PCA-EIR技术的频率响应和（或）的实现复杂性。相对于CS，我们提出的EIR技术是远远优于PCA-EIR技术。
The extrapolated impulse response (EIR) filter design based on principal component analysis (PCA) generally performs better than the non-optimal type of the traditional EIR filter design. However, no optimality was proposed in the EIR design. In this paper, an understanding of the EIR technique from the perspective of linear representation is presented. Based on the understanding, a technique for the design of the EIR filter is proposed. The proposed design is optimal in the optimal-linear-representation sense in the sequence domain. The solution set of our proposed design is theoretically derived. Within the solution set, a solution with the sub-lowest coefficient sensitivity (CS) is analytically obtained. Provided the scale factors are calculated using our proposed technique, the design of the EIR filter based on PCA (PCA-EIR) can be proved to be a solution within the solution set. Simulation experiments validate our proposed EIR technique. Our proposed EIR technique performs as well as the PCA-EIR technique with respect to the frequency response and (or) the implementation complexity. With respect to the CS, our proposed EIR technique is much better than the PCA-EIR technique.