Higher-order correlations are well known for their use in noise removal, image enhancement, and signal identification. They are generalizations of the well-known second-order correlation. The fractionalization of the second-order correlation provides some interesting features that are related to the shift-variance property of the fractional-Fourier-transform operation. This project proposes the fractionalization of the triple-correlation operation (as well as other higher-order correlations). A suggested definition as well as some applications are given. Computer simulations demonstrate some of the features this operation offers.
© 1998 Optical Society of America
David Mendlovic, David Mas, Adolf W. Lohmann, Zeev Zalevsky, and Gal Shabtay, "Fractional triple correlation and its applications," J. Opt. Soc. Am. A 15, 1658-1661 (1998)