Design of two-channel nonuniform-division maximally decimated filter banks using L₁ error criteria

The paper considers the optimal design of two-channel nonuniform-division maximally decimated filter bank (NDMTJFB) systems with linear-phase analysis/synthesis filters. Based on L₁ error criterion, the authors formulate two design problems, namely, L₁ reconstruction error and stopband response for analysis filters, L₁ reconstruction error and least-squares stopband response for analysis filters. They are usually nonlinear optimisation problems. To avoid the requirement of performing any complicated nonlinear optimisation techniques for each design, the design problems are reformulated using a linearisation scheme. As a result, finding the optimal coefficients of the analysis/synthesis filters requires the solution of linear equations. A method for solving each of the resulting design problems is developed. Simulation examples for illustration are provided.