Design of Complex All-Pass Networks Using Reméz Algorithm

In this paper we introduce a new method for designing complex all-pass digital filters. Phase error is regarded as amplitude of complex error between the designed and the desired all-pass function. Then Reméz exchange algorithm is applied to the amplitude of complex error, and it is approximated to be equiripple. Although equiripple solutions to phase approximation problems are not necessarily optimum in the Chebyshev sense, considerable design experiences show that equiripple approximations are often quite satisfactory results. Then we consider only such cases and show that the best uniform phase approximation to an arbitrarily specified phase response can be found. In this algorithm, satisfactory solution is obtained through a few iterations without any initial guess of the solution. Furthermore, as one of the complex all-pass digital filter applications, we introduce a large class of real coefficient doubly complementary IIR digital filter pairs by using a single complex all-pass digital filter, which has approximately linear phase.