Two-Channel FIR Filter Banks – A Tutorial Review and New Results

The purpose of this paper is twofold. First, a comprehensive review is performed on the existing two-channel FIR filter banks as well as on the design techniques proposed in the literature for designing these banks. We concentrate on alias-free banks. These banks can be first classified into perfect-reconstruction and nearly perfect-reconstruction banks. The nearly perfectreconstruction filter banks consist of traditional quadrature mirror filter banks with linear-phase FIR subfilters and the low-delay versions of them where the subfilters are nonlinear-phase filters. In the case of perfect-reconstruction banks, there exist conventional and low-delay biorthogonal banks as well as orthogonal banks. Second, some of the existing design techniques are either simplified or made more effective. Furthermore, a general optimization problem is stated for two-channel FIR filter banks covering all the existing banks as well as nearly perfectreconstruction conventional and low-delay biorthogonal banks. A general-purpose optimization technique is proposed for designing in a similar manner the above-mentioned two-channel aliasfree FIR filter banks. This technique enables us to minimize the maximum of the stopband energies of the two analysis filters subject to the given passband and transition band constraints of the filters as well as subject to the given allowable reconstruction error. With this technique it is straightforward to find tradeoffs between the various factors affecting the performance of the overall filter bank. Several examples are included illustrating the characteristics of the filter banks obtained by the existing synthesis schemes and the proposed design techniques.