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In this brief, the design of finite-impulse response (FIR) filter banks by semidefinite programming is discussed. The initial analysis filters are designed according to the characteristics of the input. By the design procedure, for the given set of analysis filters, synthesis filters are found so that the H∞ norm of the error system is minimized over all synthesis filters that have a prespecified order. Then, the synthesis filters obtained in the previous step are fixed and the analysis filters are found similarly. By iteration, the H∞ norm of the error system decreases until it converges to its final value.