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.