تطوير خوارزميات جديدة لمحساب السريع لتحويل هارتمي المنفصل
الشريط الجانبي للمقالة
محتوى المقالة الرئيسي
الملخص
In this paper, by using the symmetrical properties of the discrete Hartley transform (DHT), an improved radix-2 fast Hartley transform (FHT) algorithm with arithmetic complexity comparable to that of the real-valued fast Fourier transform (RFFT) is developed. It has a simple and regular butterfly structure and possesses the in-place computation property. Furthermore, using the same principles, the development can be extended to more efficient radix-based FHT algorithms. An example for the improved radix-4 FHT algorithm is given to show the validity of the presented method. The arithmetic complexity for the new algorithms are computed and then compared with the existing FHT algorithms. The results of these comparisons have shown that the developed algorithms reduce the number of multiplications and additions considerably.
المقاييس
تفاصيل المقالة
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المراجع
R. N. Bracewell, “Discrete Hartley Transform,” Journal of the Optical Society of America vol. 73, pp. 1832- 1835, 1983. DOI: https://doi.org/10.1364/JOSA.73.001832
R. N. Bracewell, “The Hartley transform,” Oxford University Press, Inc., 1986.
O. K. Ersoy and N. C. Hu, “Fast algorithms for the real discrete Fourier transform,” in International Conference on Acoustics, Speech, and Signal Processing, ICASSP-88., 1988, pp. 1902-1905 vol.3.
H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 35, pp. 849-863, 1987. DOI: https://doi.org/10.1109/TASSP.1987.1165220
R. N. Bracewell, “The fast Hartley transform,” Proceedings of the IEEE,vol. 72, pp. 1010-1018, 1984. DOI: https://doi.org/10.1109/PROC.1984.12968
H. Sorensen, D. Jones, C. Burrus, and M. Heideman, “On computing the discrete Hartley transform,” IEEE Transactions on Acoustics, Speech and Signal Processing., vol. 33, pp. 1231-1238, 1985. DOI: https://doi.org/10.1109/TASSP.1985.1164687
H. S. Hou, “The Fast Hartley Transform Algorithm,” IEEE Transactions on Computers, vol. C- 36, pp. 147-156, 1987. DOI: https://doi.org/10.1109/TC.1987.1676877
Y. H. Chan and W. C. Siu, “New fast discrete Hartley transform algorithm,” Electronics Letters, vol. 27, pp. 347-349, 1991. DOI: https://doi.org/10.1049/el:19910220
P. Duhamel and M. Vetterli, “Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 35, pp. 818-824, 1987. DOI: https://doi.org/10.1109/TASSP.1987.1165218
H. Malvar, “Fast computation of discrete cosine transform through fast Hartley transform,” Electronics Letters, vol. 22, pp. 352-353, 1986. DOI: https://doi.org/10.1049/el:19860239
C. Kwong and K. Shiu, “Structured fast Hartley transform algorithms,”IEEE Transactions on Acoustics, Speech and Signal Processing., vol. 34, pp. 1000-1002, 1986. DOI: https://doi.org/10.1109/TASSP.1986.1164896
K. J. Jones, “Design and parallel computation of regularised fast Hartley transform,” IEE Proceedings -Vision, Image and Signal Processing., vol. 153, pp. 70-78, 2006. DOI: https://doi.org/10.1049/ip-vis:20045066
G. Bi, “Split radix algorithm for the discrete Hartley transform,”Electronics Letters, vol. 30, pp. 1833- 1835, 1994. DOI: https://doi.org/10.1049/el:19941256
P. Soo-Chang and W. Ja-Ling, “Split- radix fast Hartley transform,”Electronics Letters, vol. 22, pp. 26- 27, 1986. DOI: https://doi.org/10.1049/el:19860018
A. C. Erickson and B. S. Fagin, “Calculating the FHT in hardware,” IEEE Transactions on Signal Processing, vol. 40, pp. 1341-1353, 1992. DOI: https://doi.org/10.1109/78.139240