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The design of two-channel filter banks with rational sampling factors is considered based on the use of linear-phase finite-impulse response (FIR) filters whose stop-band performances are minimized in the least squares sense. It is shown that a proper selection of the filter orders enables one to synthesize a perfect reconstruction filter bank. The optimization of the overall filter bank is carried out by properly modifying the algorithm of Dutta and Vidyasagar. The modified algorithms enables one to optimize both the perfect-reconstruction and the near perfect-reconstruction filter banks. Several examples are included illustrating the properties of the resulting optimized filter banks as well as the trade-off between the stopband attenuation and the amplitude and the aliasing errors of the optimized filter bank.