Chromatic Derivatives, Chromatic Expansions and Associated Function Spaces

Overview & Synopsis

We present the basic properties of the chromatic derivatives and the chromatic expansions as well as a motivation for introducing these notions. The chromatic derivatives are special, numerically robust linear differential operators; the chromatic expansions are the associated local expansions, which possess the best features of both the Taylor and the Nyquist expansions. This makes them potentially useful in fields involving sampled data, such as signal and image processing.