Abstract:

A linear equation system for designing hybrid filter banks (HFB) is presented on the basis of solving the coefficients of the synthesis filter banks derived from the perfect reconstruction (PR) conditions. The relationtions between the PR conditions and each different solution situations are discussed regarding the consistent and inconsistent equation case. The general solution and the lower bound of the reconstruction error are given. A second order cone programming based methodology for designing PRHFB is proposed to get the unique solution with the constrains of minimizing the stopband energy of the synthesis filter banks, which can also be used to calculate the minimum norm solution of the equation. Simulations show that this approach can get the unique solution and satisfy the system PR conditions effectively.

Key words: hybrid filter banks, perfect reconstruction, second order cone programming