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Finite-impulse response (FIR) filters are often preferred to infinite-impulse response (IIR) filters because of their various advantages in respect of stability, phase characteristic, implementation, etc. This article proposes a new method to approximate an IIR filter by an FIR filter, which directly yields an optimal approximation with respect to the H/sup /spl infin// error norm. We show that this design problem can be reduced to a linear matrix inequality. We also make a comparison via a numerical example with an existing method, known as the Nehari shuffle.