A new notion of discrete tangent, called order d discrete tangent, adapted to noisy curves, is proposed. It is based on the definition of discrete tangents given by A. Vialard in 1996, on the definition of fuzzy segments and on the linear algorithm of fuzzy segments recognition. The algorithm calculating the order $d$ discrete tangent at a point of a curve relies on simple calculations and is linear according to the number of points of the obtained tangent. From the definition of an order $d$ discrete tangent, we deduced an estimation of the normal vector and of the curvature at a point of a discrete curve for a given order d.