Performance measures and Lagrange multiplier methods to two-band PR LP filter bank design

In this paper, we study performance measures for designing two-band perfect reconstruction (PR) linear phase (LP) filter bank. Based on these performance metrics, we formulate the design problem as a nonlinear constrained optimization problem, where some metrics such as stopband energy have closed form, but the others like transition width do not. Our formulation allows us to search for designs that improve over the existing designs. More important, given user-specified performance bounds such as maximal transition width, we are able to design filter banks if solutions exist, and trade-off among different performance metrics can be easily achieved. Finally, many experimental results show feasibility and efficiency of our filter bank design method