OPTIMAL SIGNAL RECONSTRUCTION IN NOISY FILTER BANK SYSTEMS - MULTIRATE KALMAN SYNTHESIS FILTERING APPROACH

A multirate Kalman synthesis filter is proposed in this paper to replace the conventional synthesis filters in a noisy filter bank system to achieve optimal reconstruction of the input signal, Based on an equivalent block representation of subband signals, a state-space model is introduced for anM-band filter bank system with subband noises, The composite effect of the input signal, analysis filter bank, decimators, and interpolators is represented by a multirate state-space-model, The input signal is embedded in the state vector, and the corrupting noises in subband paths are generally considered as additive noises, Hence, the signal reconstruction problem in the M-band filter bank systems with subband noises becomes a state estimation procedure in the resultant multirate state-space model, The multirate Kalman filtering algorithm is then derived according to the multirate state-space model to achieve optimal signal reconstruction in noisy filter bank systems, Based on the optimal state estimation theory, the proposed multirate Kalman synthesis filter provides the minimum-variance reconstruction of the input signal, Two numerical examples are also included, The simulation results indicate that the performance improvement of signal reconstruction in noisy filter bank systems is remarkable.