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In this brief, the least pth-phase error criterion is adopted to design digital infinite-impulse-response all-pass filters to have an arbitrarily prescribed phase response. First, an iterative reweighted least-squares method is used to design an unconstrained all-pass filter whose optimal filter coefficients are obtained by solving a set of linear simultaneous equations in each iteration. Then, the proposed method is extended to design a constrained all-pass filter. Finally, a design example of the Hilbert transformer is demonstrated to illustrate the effectiveness of the new design method.