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 an M-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.