The topics of fractional (order) derivative and its digital implementations are studied from the view point of signal processing in this paper. A brief survey on fractional differentiation and integration is given

some basic concepts of the fractional calculus and some typical definitions of the fractional derivative are reviewed.Next the digital implementation approaches of fractional differentiators are discussed in detail. Some new problems

which would been encounted in the design of the fractional differentiators

and some new concepts

such as the odd symmetric differentiators and even symmetric differentiators are proposed.Finally

future works are reviewed in the concluding remarks.