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In this note, a finite impulse response (FIR) filter design problem is considered. The signals to be filtered are assumed to be corrupted by the channel noise. In addition, the channel characteristics are assumed to contain uncertainties. The linear matrix inequalities approach is adopted to provide two optimization procedures for designing H∞ optimal filters and robust H∞ filters subject to filter output envelope constraints. A numerical example is presented to illustrate the proposed filter design methods.