Degree, ripple, and transition width of elliptic filters
Miroslav Vlček, Rolf Unbehauen · IEEE Transactions on Circuits and Systems · 1989
Simple analytic formulas inverting the degree education in both analog and digital equiripple filter approximations are presented. The inversion of the degree equation which is usually expressed as a ratio of theta functions, known in classical mathematics as a modular equation, is obtained in form of a finite product of Jacobian functions. From the numerical point of view it allows the recalculation of the parameters which control the optimization using an efficient arithmetic-geometric-mean procedure only. For the evaluation of k/sub 1/ from n and K (k', respectively) the zeros of the characteristic function are used and no additional computation is required.>