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A novel method for designing recursive allpass digital filters is presented. This method uses cepstral coefficients to design the allpass filter. For a stable allpass filter, the denominator polynomial must be of minimum phase. For a minimum phase polynomial the magnitude function and the group delay function are related through the cepstral coefficients. Hence, given the group delay function, the cepstral coefficients corresponding to the denominator polynomial part are first determined. From the cepstral coefficients the minimum phase denominator polynomial coefficients are determined through a nonlinear recursive difference equation.