  In a recent article, we showed that trigonometric shearlets are able to
detect directional step discontinuities along edges of periodic characteristic
functions. In this paper, we extend these results to multivariate periodic
functions which have jump discontinuities in higher order directional
derivatives along edges. In order to prove suitable upper and lower bounds for
the shearlet coefficients, we need to generalize the results about
localization- and orientation-dependent decay properties of the corresponding
inner products of trigonometric shearlets and the underlying periodic
functions.
