Hybrid Filter Banks With Fractional Delays: Minimax Design and Application to Multichannel Sampling

This paper is motivated by multichannel sampling applications. We consider a hybrid filter banks consisting of a set of fractional delays operators, slow A/D converters with different antialiasing filters, digital expanders, and digital synthesis filters (to be designed). The synthesis filters are designed to minimize the maximum gain of a hybrid induced error system. We show that the induced error system is equivalent to a digital system. This digital system enables the design of stable synthesis filters using existing control theory tools such as model-matching and linear matrix inequalities. Moreover, the induced error is robust against delay estimate errors. Numerical experiments show the proposed approach yields better performance compared to existing techniques.