On the search for compatible numbers in the design of maximally decimated perfect reconstruction non-uniform filter bank

The theory and design of critically sampled perfect reconstruction (PR) uniform filter bank (FB) is well established. However, the principles of non-uniform PR FB are still an active research topic. A number of necessary (compatibility) conditions have been identified, which any set of integer decimation factors must satisfy for existence of a realizable maximally-decimated perfect-reconstruction non-uniform filter bank. The search for a compatible-set, in the neighborhood of a desired set of decimation factors, can be computationally prohibitive, as it is exponential to the number of filters in the bank. We propose a branch-and-bound algorithm to efficiently search for compatible-sets. We present experimental results for a compatible set of a 26-filter bank, matching the critical bands of the human auditory system very closely.