Multicriterion optimized QMF Bank design

The quadrature mirror filter (QMF) bank with multicriterion constraints such as minimal aliasing and/or minimal error coding is among the most important problems in filterbank 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 this problem can be reduced either to convex linear matrix inequality (LMI) optimization (when filters are of nonlinear phase) or to semi-infinite linear (SIP) programming (when filters are of linear phase), which can be very efficiently solved either by the standard LMI solvers or our previously developed SIP solver. The proposed computationally tractable optimization formulations are confirmed by several simulations.