Filter realization using a generalized lagrange polynomial representation

Abstract

SUMMARYA polynomial representation using a set of generalized Lagrange polynomials for a basis is considered as an alternative to the natural representation. This new representation, which is employed in a previously described APL filter design package,* is considered in detail, here, with regard to its algebraic and numerical properties for solving the realization problem of electrical filter synthesis. The necessary polynomial operations for filter realization are described in this representation. Then vector space algorithms are presented for these operations. The accuracy obtained from this representation is discussed. Advantages in both accuracy and simplicity of the new algorithms are noted.