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Minimax design of 1-dimensional recursive digital filters is currently achieved by using iterative methods based on linear or nonlinear programming. The methods need extensive computation and their convergence cannot be always guaranteed. Recently Charalambous developed a closed form approach for designing minimax elliptic filters. In the present paper, the Charalambous approach is extended into developing a closed form approach for designing 1-dimensional recursive minimax digital filters of any given approximation type satisfying prescribed specifications. The amount of computation needed by the new approach is insignificant. A general-purpose computer program has also been developed that embodies the classical and minimax Butterworth, ChebyÂ¿chev and elliptic approximations.