Discrete chromatic series

Abstract

Chromatic series are series expansions in which the coefficients are linear combinations of derivatives of a function. They were introduced by Ignjatovic (Introduction to Signal Processing Based on Differential Operators, Tech. Rep. 1, Kromos Technology, available at http://www.kromos.com, February 2001.) as a replacement for Taylor's series and are based on orthogonal polynomials. However, real data usually involves the values of a function and not its derivatives which are needed in both theories. In this article, we replace the derivatives by discrete values in the calculations of the coefficients.