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Much attention has recently been given to the construction of signal-adapted orthonormal filter banks designed to optimize a particular objective function such as coding gain or a multiresolution criterion. For certain classes of filter banks, the optimum solution is a principal component filter bank (PCFB), which is simultaneously optimal for several objectives including the ones mentioned above. However, for the class of finite impulse response (FIR) filter banks, a PCFB in general does not exist. For this case, numerical techniques must be employed to find an optimum filter bank for a particular objective. In this paper, we present an iterative method for designing an overdecimated FIR filter bank optimized for energy compaction. The proposed algorithm is an eigenfilter method that is low in computational complexity. Simulation results show the merit of the proposed method, in that as the filter order increases, the filters designed behave more and more like those of the infinite order PCFB.