Analysis of the fractional Hilbert transform

Abstract

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 can select which edges are enhanced and to what degree the edge enhancement occurs. Although experimental results of this selective edge enhancement were presented, there was no explanation of this phenomenon. We analyze a one-dimensional fractional Hilbert transform acting on a one-dimensional rectangle function and show how it produces an output image that is selectively edge enhanced.