The optimally reconstructed design of the causal stable synthesis filters in the M-band maximally decimated filter bank system

In the traditional design of the M-band maximally decimated filter bank system, the resulting designed synthesis filters may be unstable. Based on the least square criterion and employing the calculus of variation and the spectral factorization techniques, a modified synthesis filter can be obtained. A causal stable synthesis filter bank is proposed to replace the conventional synthesis filter bank system to achieve optimal reconstruction of the input signal. With this approach, a general form of the two-band filter bank system can be obtained. An illustrated example is present. The stability of all synthesis filter bank can be guaranteed by the proposed approach. However, the reconstructed performance is system dependent. For the same system, the reconstructed performances are also frequency dependent. The complete study of the working frequency can be referred to improve the system performance