Design of perfect-reconstruction hybrid filter banks: A second-order cone programming approach

In this paper, we present a new convex programming design methodology for hybrid filter banks (HFB) by solving a linear equation system derived from the perfect reconstruction (PR) conditions. The relationship 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 to the error of reconstruction are given. A second order cone programming (SOCP) based algorithms for designing PR HFB is proposed to get the exact solution with the constrained of stopband energy minimum which can also be used to calculate the minimizing norm solution of the equation. Finally, we consider some design examples and evaluate their performance.