基于加权最小二乘正则化方法的混合滤波器组最优化设计

Hybrid Filter Banks Optimization Design Using Regularization  Weighted Least Squares Solving

  • 摘要: 模拟分析滤波器的实现误差以及数字综合滤波器有效阶数实现的设计误差造成的病态问题都将影响混合滤波器组(HFB)的重构效果。提出一种新的满足近似完美重构的基于加权最小二乘(WLS)正则化算法的IIR形式综合滤波器设计方法。该算法根据误差量二阶统计特性采用WLS算法抑制滤波器实现误差以及随机噪声等扰动因素影响,使得到的综合滤波器组频域响应解的加权误差平方和最小化,并通过Tikhonov正则化方法优化解的稳定性。提出一种IIR类型综合滤波器设计算法,并利用正则化方法优化滤波器系数,减小设计误差。该方法可应用于过采样HFB的设计。仿真结果表明该算法的有效提高系统鲁棒性和改善重构性能。

     

    Abstract:  The ill-posed problems caused by analogy analysis filters realization error and digital synthesis filter banks fitting error for limited order,which usually impact the reconstruction performance of the hybrid filter banks (HFB). A novel regularization criterion for designing IIRtype synthesis filter banks based on weighted least squares (WLS) are proposed, which satisfying near perfect reconstruction. Based on the second-order-statistics, the disturbers which caused by realization and random noise can be restrained by means of the WLS. So the weighted mean squares of synthesis filter banks frequency responses can be Minimize. The regularization criterion can overcome the instability solution of WLS effectively. A novel approach for designing IIR-type filters are given, which can optimize the coefficients of filters by means of the regularization method and reduce the implement error. This approach can also be used in designing over-sampling HFB. The simulation results show that this approach can improve the system robust and reconstruction performance significantly.

     

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