A General Class of Optimal Polynomials Related to Electric Filters

A class of optimal polynomials is obtained satisfying general constraints imposed on the pass and stop bands of low-pass and band-pass electric filters. Mathematically speaking, the x-axis is divided into intervals called bands. One of them, the pass band, is divided into sub-intervals with various upper-bound constraints on the value of the polynomial. Others, the stop bands, are divided into sub-intervals with lower-bound constraints. The pass and stop bands are separated by transition bands whose widths are minimized by the optimal polynomials. Algorithms are presented to obtain the optimal polynomials and they are proved to converge. 1