基于加权总体最小二乘正则化方法的混合滤波器组最优化设计

模拟分析滤波器组的实现欠理想、系统噪声以及数字综合滤波器有效阶数实现所带来的系统误差均有可能造成混合滤波器组的设计出现解不稳定、无唯一解等病态问题，影响混合滤波器组的准确重构效果。本文首先给出了满足准确重构条件下，以综合滤波器组频域响应为求解变量的混合滤波器组线性求解模型。针对线性方程中系数矩阵以及目标向量受扰动误差影响特点，提出一种新的基于加权总体最小二乘正则化算法的IIR形式综合滤波器设计方法。算法以系统扰动误差最小化为目标函数，根据随机误差变量的二阶统计特性，采用加权总体最小二乘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正则化方法优化病态情况下方程组解的稳定性。提出一种IIR类型的综合滤波器系数的求解算法，并利用正则化方法优化滤波器系数，提高系统稳定性。该方法可应用于过采样混合滤波器组的设计。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。 

Hybrid Filter Banks Optimization Design Using Regularization Weighted Total Least Square Solving

The nonideal realization of analogy analysis filters, system noise and digital synthesis filter banks fitting error for limited order，which usually impact the reconstruction performance of the hybrid filter banks and make the ill-posed problems happened with the solution unstable and non unique solution exist. A linear equation system for hybrid filter banks is presented by solving the frequency response of the synthesis filter banks derived from the perfect reconstruction conditions. A novel regularization criterion for designing IIR-type synthesis filter banks based on weighted least squares methodology are proposed for solving the disturbance in the coefficient matrix and object vector of the linear equation. With the objection function of minimizing system error, the disturbers which caused by realization error and random noise can be restrained by means of the weighted least squares based on the second order statistics. So the weighted mean squares of synthesis filter banks frequency responses can be Minimize. The regularization criterion can overcome the instability solution of weighted least squares 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 improve the stability of hybrid filter banks. This approach can also be used in designing over-sampling hybrid filter banks. The simulation results show that this approach can improve the system robust and reconstruction performance significantly.