RATIONAL FUNCTION APPROXIMATION OF POLYNOMIALS WITH EQUIRIPPLE ERROR
Abstract
A method was proposed whereby any polynomial can be approximated in an equitable manner by a rational function. The properties and form of this rational function are discussed. Several examples are used to illustrate the theory. Most of these examples are chosen so that the approximating rational function can be identified as a network function part; in particular, the group delay was given special emphasis. The ideal group delay vs. frequency characteristic of filter is a constant. This type of group delay is approximated in an equitable manner. In addition, a numerical scheme is proposed such that from a given crude equitable approximation a more exact solution can be obtained. An ex ample used to illustrate this approach is the problem of compensating the non-constant group delay characteristics of a sharp- cutoff, low pass filter.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1963
- Accession Number
- AD0402778
Entities
People
- Deverl Humpherys
Organizations
- University of Illinois Urbana–Champaign