Some new aspects of filters for filter banks

The present paper deals with the design of filters for use in filter banks, i.e., with certain constraints on their transition bands. The goal is to achieve a baseband frequency response of a back-to-back analysis/synthesis filter bank system that is ideally flat in magnitude and linear in phase. Using the proposed method, this is possible for conventional polyphase filter banks, single-sideband (SSB) filter banks, and generalized quadrature mirror filter (GQMF) banks. The method provides several options, one of them even yielding subsystems with linear phase. In contrast to most previous approaches to this topic, the described design procedure is an analytical one and is not based on optimizations or iterative algorithms. Furthermore, two families of window sequences are proposed for use in the design procedure mentioned above, but are also suitable for any windowed Fourier filter design.