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Original Articles

Discrete chromatic series

Pages 579-594 | Received 17 Nov 2009, Accepted 07 Jan 2010, Published online: 29 Jun 2010
 

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.

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