Efficient Computation of Frame Bounds Using LMI-Based Optimization

This correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction (PR) filter banks (FBs). It first shows that computation of the optimal frame bounds for complex-valued oversampled PR FBs can be formulated as a convex optimization subject to complex-valued linear matrix inequality (LMI) constraints and solved by effective interior-point algorithms. It then deals with discrete-time Weyl-Heisenberg (WH) frames to compute bounds on the WH frames by real-valued LMI optimization. The WH frames are closely related to modulated FBs and have complex coefficients. Four examples are given to illustrate the generality and effectiveness of the proposed method.