Unified approach to the design of quadrature-mirror filters

A unified approach to the design of linear- and nonlinear-phase QMFs is developed. Formulated as an optimization problem, the design procedure is shown to translate into an eigenvalue-eigenvector problem. To find the optimal filter an algorithm is presented, which typically converges in a few tens of iterations. The flexibility of our design procedure permits several practical extensions to be made readily. These are (a) inclusion of frequency-weighted stop band energy criteria, and (b) inclusion of finite word-length constraints. We have successfully used our filters to applications such as image coding and analysis; here, their use in wavelet-series analysis of oceanographic data is demonstrated