Design of all-pass networks using Remez algorithm

A novel method for designing digital all-pass networks is introduced. Some design methods of all-pass networks have been proposed. However, the drawbacks of these schemes include the need for initial solutions and heavy computations. On the other hand, the design method proposed here finds the best uniform phase approximation through several iterations by solving linear equations. Phase error is regarded as the amplitude of complex error between the designed and desired all-pass function. Then, the Remez exchange algorithm is applied to the amplitude of the complex error, and it is approximated to equiripple. Maximum phase error is minimized, and the best uniform phase approximation in the Chebyshev sense is found. An optimal solution is obtained through several iterations without any initial guess of the solution.