Minimax design of hybrid multirate filter banks

Hybrid multirate filter banks which consist of analog analysis filters, slow A/D converters, digital expanders, and digital synthesis filters are studied in this paper. The synthesis filters are designed to minimize the maximum energy gain of the error system, suitably weighted, between the filter bank and a fast A/D converter with some time delay. This hybrid and multirate problem is reduced to one of H^∞ optimization involving only linear time-invariant, discrete-time systems, which is then solvable. An example is discussed and studied in detail to illustrate aspects in the design process