The Hilbert transform is of interest for image-processing applications
because it forms an image that is edge enhanced relative to an input
object. Recently a fractional Hilbert transform was introduced that ca
n select which edges are enhanced and to what-degree the edge enhancem
ent occurs. Although experimental results of this selective edge enhan
cement were presented, there was no explanation of this phenomenon. We
analyze a one-dimensional fractional Hilbert transform acting on a on
e-dimensional rectangle function and show how it produces an output im
age that is selectively edge enhanced. (C) 1998 Optical Society of Ame
rica.