Nonuniform filter bank design with noises

This work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noises. Three main nonuniform filter bank systems, i.e., filter-block decimator (FBD) structure, upsamplerfilter-downsampler (UFD) structure, and tree structure, are included in this study. According to different operating conditions, two different signal reconstruction problems for nonuniform filter bank systems with noises under the unknown but identifiable input signal model and the unknown input signal model are discussed, respectively. At the first stage, a unified block state space model for different nonuniform filter bank systems with noises is developed. Then, by incorporating the identified input signal model with this unified state space model and appropriate choice of the augmented state vector, the signal reconstruction problem is reduced to an equivalent state estimation problem for resulting augmented systems if the input signal is identifiable. If the input signal is lacking in modeling, the signal reconstruction is discussed from the minimax estimation point of view. Two state estimation techniques involving robust Kalman filtering and H1 filtering are employed, respectively, to treat the signal reconstruction problem of nonuniform filter bank systems according to different a priori knowledge of the input signal. Finally, several numerical examples are presented to illustrate the proposed algorithms and exhibit the performances.