Nonuniform multirate filter banks: analysis and design with an ℋ∞ performance measure

A general multirate filter-bank system with multiple channels and nonuniform bands is studied with the reconstruction performance measured by the worst-case energy gain (ℋ_∞ norm) of the error system between the multirate system and a pure time-delay system. Using blocking and polyphase decomposition, we associate with the multirate system an equivalent linear time-invariant (LTI) system whose transfer matrix can be computed by a simple procedure. Based on this LTI system, the optimal design problem can be reduced to one of ℋ_∞ optimization, which can be solved by ready-made software in many cases. For illustration, optimal synthesis filters are designed for a two-channel example, and their properties are studied in detail