The problem of designing recursive digital filters with optimized word length coefficients to meet arbitrary, prescribed magnitude characteristics in the frequency domain is numerically investigated. The continuous nonlinear programming problem is formulated as an unconstrained minimax problem using the Bandler-Charalambous approach, and Dakin's branch-and-bound technique is used in conjunction with Fletcher's unconstrained minimization program to discretize the continuous solution. The objective function to be minimized is directly concerned with the word lengths of the coefficients, which are also introduced as variables.††This paper was presented at the Eighth Annual Princeton Conference on Information Sciences and Systems, Princeton, N.J., March 28–29, 1974.