Equiripple magnitude approximation for low‐pass IIR digital filters with prescribed group delay
Kiyoshi Nishikawa, Chang-Seok Choi · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1990
Abstract An efficient algorithm is proposed for approximating the magnitude of the low‐pass IIR digital filter with prescribed group delay in equiripple. Prescribed group delay characteristics can be realized by placing in the denominator of the transfer function a polynomial expression designed to have such characteristics. For amplitude characteristics we approximate it to obtain equiripple using a linear‐phase polynomial in the numerator. Equiripple magnitude approximation is done separately for the passband and for the stopband and all the characteristics are made equiripple by several times of iterations. In this simple method the auxiliary complex plane is utilized and in each the transformed transfer function is expressed as the sum of objective magnitude 1 and the error function for it. By assigning an all‐pass function to an approximation function of the error function, equiripple characteristics are realized. By approximation in the stopband, good equiripple characteristics can be obtained even if all the degrees of freedom are used. On the other hand, since the approximation in the passband deviated largely from equirippleness, a method is presented for improving ripple characteristics by reducing the degree of freedom by one. As a design example, a filter of order 10 is given.