Structure and design of two-channel filter banks derived from a triplet of halfband filters

A novel approach for the construction of two-channel one-dimensional (1-D) biorthogonal filter banks is described. This approach is intended to help overcome limitations in an otherwise effective set of recently proposed techniques while retaining the advantages of a simple design and feature-rich structure. The novelty of the method rests on the use of a triplet of halfband filters, which are combined in a convenient form of the transfer function with adjustable parameters that provide the necessary flexibility in obtaining the desired response. Design procedures are described for the construction of the filter banks by casting the approximation problem in a form that easily lends itself to Remez exchange algorithm. In these design procedures, the analysis and synthesis filters can be either finite-duration impulse response, infinite-duration impulse response, or a hybrid. Examples of design of 1-D filter banks and extension of the technique to two-dimensional diamond filter banks are presented. Finally, subband image-coding examples are given to demonstrate the advantage of the proposed filter-bank structure.