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The use of optimization techniques for designing digital filters has become widespread in recent years. Among the techniques that have been used include steepest descent methods, conjugate gradient techniques, penalty function techniques, and polynomial interpolation procedures. The theory of linear programming offers many advantages for designing digital filters. The programs are easy to implement and yield solutions that are guaranteed to converge. There are many areas of finite impulse response (FIR) filter design where linear programming can be used conveniently. These include design of the following: filters of the frequency sampling type; optimal filters where the passband and stopband edge frequencies of the filter may be specified exactly; and filters with simultaneous constraints on the time and frequency response. The design method is illustrated by examples from each of these areas.