Recursive digital filters having equiripple group delay

In a recent paper Thiran has proposed a method for the approximation of constant group delay in an equiripple manner, based on the method of Ulbricht and Piloty. A different, conceptually simpler solution to the same problem is proposed. The solution is based on an algorithm of the pole-shifting type, related to Remez's second algorithm. The choice of initial conditions is discussed and numerical solutions are given.