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This paper discusses the use of linear programming techniques for the design of infinite impulse response (IIR) digital filters. In particular, it is shown that, in theory, a weighted equiripple approximation to an arbitrary magnitude function can be obtained in a predictable number of applications of the simplex algorithm of linear programming. When one implements the design algorithm, certain practical difficulties (e.g., coefficient sensitivity) limit the range of filters which can be designed using this technique. However, a fairly large number of IIR filters have been successfully designed and several examples will be presented to illustrate the range of problems for which we found this technique to be useful.