  In recent years it has turned out that shearlets have the potential to
retrieve directional information so that they became interesting for many
applications. Moreover the continuous shearlet transform has the outstanding
property to stem from a square integrable group representation. However, to use
shearlets and the shearlet transform for reasonable applications one needs fast
algorithms to compute a discrete shearlet transform. In this tutorial we
present the steps towards an implementation of a fast and finite shearlet
transform that is only based on the FFT. Using band-limited shearlets we
construct a Parseval frame that provides a simple and straightforward inverse
shearlet transform. We provide all proofs and discuss several aspects of our
implementation.
