A digital all-pass transfer function with all possible coefficient combinations

Characteristics of a second-order digital all-pass network with all possible combinations of two coefficients are discussed, and the constraints that the system should be stable and the group delay characteristic on extremum are described. Approximation formulas are given for the maximum group delay and for the angular frequency at which the group delay attains its maximum value. Digital all-pass transfer functions realizable with two finite wordlength multipliers and their maximum group delay characteristics are also described.