SDP for multi-criterion QMF bank design

The quadrature mirror filter (QMF) bank, with multi-criterion constraints such as minimal aliasing and/or minimal error coding, is among the most important problems in filter bank design, for solving which linear algebra-based methods are still heuristic and do not always work, especially for large filter length. It is shown in this paper that when filters are of nonlinear phase, this problem can be reduced to convex linear matrix inequality (LMI) optimization, which can be very efficiently solved either by the standard LMI solvers or our previously developed solver. The proposed computationally tractable optimization formulations are confirmed by several simulations.