Linear phase filter bank design using LMI-based H∞ optimization

This paper is concerned with the design of nearly linear phase two-channel filter banks. Exactly linear phase finite-impulse response or nearly linear phase infinite-impulse response (IIR) filters are employed in analysis filter banks, and nearly linear phase IIR synthesis filter banks are designed such that the overall filter banks are also nearly linear phase. The filter bank design problem is formulated as a H_∞ norm minimization of the difference between the pure delay and the products of some polyphase components. The H_∞ norm optimizing problem is converted to a series of linear matrix inequalities (LMIs) and solved using semidefinite programming. The magnitude, phase and aliasing distortions are all incorporated in the design procedure.