  We describe a new wavelet transform, for use on hierarchies or binary rooted
trees. The theoretical framework of this approach to data analysis is
described. Case studies are used to further exemplify this approach. A first
set of application studies deals with data array smoothing, or filtering. A
second set of application studies relates to hierarchical tree condensation.
Finally, a third study explores the wavelet decomposition, and the
reproducibility of data sets such as text, including a new perspective on the
generation or computability of such data objects.
