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An efficient general-purpose optimization approach is proposed for designing two-channel finite impulse response (FIR) filterbanks. This technique can be used for optimizing two-channel FIR filterbanks in all alias-free cases proposed in the literature. The generalized problem is to minimize the maximum of the stopband energies of the two analysis filters subject to the given passband and transition band constraints and the given allowable reconstruction error. Therefore, in addition to the perfect-reconstruction filterbanks, nearly perfect-reconstruction banks can be optimized in a controlled manner. The optimization is carried out in two steps. In the first step, for the selected type of the filterbank, a good starting-point filterbank for further optimization is generated using an existing design scheme. The second step involves optimizing the filterbank with the aid of a modified Dutta-Vidyasagar (1977) algorithm. Several examples are included, illustrating the efficiency and the flexibility of the proposed approach.