Radix-2 × 2 × 2 algorithm for the 3-D discrete Hartley transform

• Published in: IEEE transactions on signal processing 2001-12, Vol.49 (12), p.3145-3156
• Main Authors: Boussakta, S., Alshibami, O.H., Aziz, M.Y.
• Format: Article
• Language: English
• Subjects: Algorithms; Arithmetic; Butterflies; Derivation; Mathematical analysis; Signal processing; Transforms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.969521

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 2 2 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