The design of a class of prefect reconstruction two-channel FIR and wavelets filterbanks using constrained least squares method and semidefinite programming

Abstract

This paper proposes two new methods for designing a class of 2-channel PR FIR filterbanks and wavelets with K-regularity of high order. The K-regularity constraints are expressed as a set of linear constraints in the design variables. The first method formulates the design problem as a quadratic programming problem with linear equality constraints (QPLC), which can be solved using the method of Lagrange multiplier. The second design method employs the minimax error criteria and solves the design problem as a semidefinite programming problem (SDP). By removing the redundant variables, the equality constraints are automatically imposed into the design problem. The optimization problem is then formulated as a linear convex objective function subject to a union of affine set which can be represented by a set of linear matrix inequalities. Hence they can be solved using existing SDP solver. Design examples are given to demonstrate the effectiveness of the proposed methods.