Generalizations of Chromatic Derivatives and Series Expansions

A.I. Zayed
2010 IEEE Transactions on Signal Processing  
Chromatic derivatives and series expansions of bandlimited functions have recently been introduced as an alternative representation to Taylor series and they have been shown to be more useful in practical signal processing applications than Taylor series. Although chromatic series were originally introduced for bandlimited functions, they have now been extended to a larger class of functions. The n-th chromatic derivative of an analytic function is a linear combination of the kth ordinary
more » ... kth ordinary derivatives with 0 ≤ k ≤ n, where the coefficients of the linear combination are based on a suitable system of orthogonal polynomials. The goal of this article is to extend chromatic derivatives and series to higher dimensions. This is of interest not only because the associated multivariate orthogonal polynomials have much reacher structure than in the univariate case, but also because we believe that multidimensional case will find natural applications to fields such as image processing and analysis. 2000 Mathematics Subject Classification. Primary 41A58, 42C15; Secondary 94A12, 94A20.
doi:10.1109/tsp.2009.2038415 fatcat:rex5eyn2ezg27dwn7k2ktk26ky