Iterative Method for the Design of DFT Filter Bank

Multirate adaptive filters have numerous advantagessuch as low computational load, fast convergence, and parallelismin the adaptation. Drawbacks when using multirate processing aremainly related to aliasing and reconstruction effects. These effectscan be minimized by introducing appropriate problem formulationand employing sophisticated optimization techniques. In thispaper, we propose a formulation for the design of a filter bankwhich controls the distortion level for each frequency componentdirectly and minimizes the inband aliasing and the residual aliasingbetween different subbands. The advantage of this problem formulationis that the distortion level can be weighted for each frequencydepending on the particular practical application.Anew iterativealgorithm is proposed to optimize simultaneously over boththe analysis and the synthesis filter banks. This algorithm is shownto have a unique solution for each iteration. For a fixed distortionlevel, the proposed algorithm yields a significant reduction in boththe inband aliasing and the residual aliasing levels compared to existingmethods applied to the numerical examples.