Adaptive filtering using filter banks

This paper derives a theory for adaptive filters which operate on filter bank outputs, here called filter bank adaptive filters (FBAFs). It is shown how the FBAFs are a generalization of transform domain adaptive filters and adaptive filters based on structural subband decompositions. The minimum mean-square error performance and convergence properties of FBAFs are determined as a function of filter bank used. A parametrization for a class of FIR perfect reconstruction filter banks is derived which is used to design FBAF´s having optimal error performance given prior knowledge of the application. Simulations are performed to illustrate the derived theory and demonstrate the improved error performance of the FBAFs relative to the LMS algorithm, when prior knowledge is incorporated