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Radix-2 x 2 x 2 algorithm for the 3-D discrete hartley transform

Boussakta, S., Alshibami, O.H. and Aziz, M.Y. (2001) Radix-2 x 2 x 2 algorithm for the 3-D discrete hartley transform. IEEE Transactions on Signal Processing, 49 (12). pp. 3145-3156. ISSN 1053-587X

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Abstract

The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one- and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 2X 2X algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Electronic & Electrical Engineering (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 07 Oct 2005
Last Modified: 04 Jun 2014 10:27
Published Version: http://dx.doi.org/10.1109/78.969521
Status: Published
Refereed: Yes
Identification Number: 10.1109/78.969521
URI: http://eprints.whiterose.ac.uk/id/eprint/707

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