The design of two-channel perfect reconstruction FIR triplet wavelet filter banks using semidefinite programming

This paper proposes a new method for designing 2-channel PR linear-phase/low-delay FIR triplet wavelet filterbanks with user-defined cutoff frequency and prescribed number of K-regularity. The magnitudes of the analysis/synthesis filters pair at ω = π/2 can be set to any desired value controlled by a certain number of parameters using the triplet structure. The K-regularity conditions are expressed as a set of linear equality constraints in the variables to be optimized. The design method employs the minimax error criteria and solves the design problem as a semidefinite programming (SDP) optimization. By removing the redundant variables, the linear 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 (LMI). Hence they can be solved using an existing SDP solver. Design examples are given to demonstrate the effectiveness of the proposed method.