Title :
Degree, ripple, and transition width of elliptic filters
Author :
Vlcek, Miroslav ; Unbehauen, Rolf
Author_Institution :
Lehrstuhl fur Allgemeine und Theor. Elektrotech., Erlangen-Nurnberg Univ., West Germany
fDate :
3/1/1989 12:00:00 AM
Abstract :
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.<>
Keywords :
digital filters; filters; transfer functions; Jacobian functions; analog; characteristic function; degree equation; digital; efficient arithmetic-geometric-mean procedure only; elliptic filters; equiripple filter approximations; finite product; modular equation; theta functions; transition width; Charge measurement; Chebyshev approximation; Current measurement; Equations; Filters; Jacobian matrices; MOS capacitors; Measurement standards; Solid state circuits; Switching converters;
Journal_Title :
Circuits and Systems, IEEE Transactions on
