  This paper presents the basic properties of chromatic derivatives and
chromatic expansions and provides an appropriate motivation for introducing
these notions. Chromatic derivatives are special, numerically robust linear
differential operators which correspond to certain families of orthogonal
polynomials. Chromatic expansions are series of the corresponding special
functions, which possess the best features of both the Taylor and the Shannon
expansions. This makes chromatic derivatives and chromatic expansions
applicable in fields involving empirically sampled data, such as digital signal
and image processing. The first section of this paper is a 2 page extended
abstract.
