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The application of the Bandler-Charalambous method using extremely large values of p, typically 10,000 to the problem of choosing the coefficients of a recursive digital filter to meet arbitrary specifications on the magnitude characteristics, is described. The Fletcher (1970) method is used in conjunction with least pth optimization and is compared with the well-known Fletcher-Powell method. Some relevant design ideas, such as local optimality checking by perturbation, increasing the order complexity of the filter through growing filter sections, and meeting the stability requirements by using a pole inversion technique, have been implemented. A general description of a computer program package that uses these ideas, along with some illustrative examples are given.