Design of filterbanks using a fast optimization approach

An optimization approach is proposed which can be used to design all types of filter banks. The design problem is formulated as the iterative minimization of two quadratic functions consisting of the perfect reconstruction (PR) condition and the energy in the filters´ stopband areas. By relaxing the frequency specifications on the filters´ passband areas, the performance indexes are becoming quadratic functions and can be efficiently minimized. This might result in the presence of ripple inside the filter bank, but the output would be ripple-free provided that the PR conditions are satisfied. The performance of the proposed algorithm (available in [14]) is illustrated with four examples indicating that a good filter bank design can be obtained very fast.