Ripple and transition-width trade-off in the design of elliptic filters

In the design of elliptic function filters, passband and stopband specifications are used to determine the order of the filter. In standard design methods, the calculated order is a fraction and the actual filter is designed by using an order which is the smallest integer greater than the calculated fraction. The authors shown how one can use this effective increase to further reduce either the passband ripple, the stopband ripple, or the transition bandwidth to give a well-defined optimal approximation. It is shown how to start with the order and design an optimal elliptic function filter by minimizing any one of the other approximation measures. The authors posed four optimal filter design problems using the Chebyshev error criterion in the passband and stopband. An algorithm is described that allows the solution of these problems using Jacobian elliptic function theory.<>