Fast Hankel transform by fast sine and cosine transforms: the Mellin connection

IEEE Transactions on Signal Processing

Volumn 48, Issue 6, 2000, Pages 1695-1701

  Knockaert, Luc ^a  

^a IMEC   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INVERSE PROBLEMS; MATHEMATICAL TRANSFORMATIONS; SAMPLING;

HANKEL TRANSFORM; MELLIN TRANSFORM; SINE TRANSFORM;

SIGNAL PROCESSING;

EID: 0033729344     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.845927     Document Type: Article

References (26)

1. A. Papoulis, Systems and Transforms with Applications in Optics. New York: McGraw-Hill, 1968.
2. L. M. Brekhovskikh, Waves in Layered Media. New York: Academic, 1960.
3. R. Hsieh and J. Kuo, "Fast full-wave analysis of planar microstrip circuit elements in stratified media," IEEE Trans. Microw. Theory Tech., vol. 46, pp. 1291-1297, Sept. 1998.
4. K. A. Michalski, "Extrapolation methods for Sommerfeld integral tails," IEEE Trans. Antennas Propagat., vol. 46, pp. 1405-1418, Oct. 1998.
5. W. E. Higgins and D. C. Munson, "A Hankel transform approach to tomographic image reconstruction," IEEE Trans. Med. Imag., vol. 7, pp. 59-72, 1988.
6. M. J. Crée and P. J. Bones, "Algorithms to numerically evaluate the Hankel transform," Comput. Math. Appi, pp. 1-12, 1993.
7. A. E. Siegman, "Quasi fast Hankel transform," Opt. Lett., vol. 1, no. 1, pp. 13-15, July 1977.
8. J. P. Talman, " Numerical Fourier and Bessel transforms in logarithmic variables," J. Comput. Phys., vol. 29, pp. 35-48, 1978.
9. H. K. Johansen and K. Sorensen, "Fast Hankel transforms," Geophys. Prospect., vol. 27, pp. 876-901, 1979.
10. A. Agnesi, G. C. Reali, G. Patrini, and A. Tomaselli, "Numerical evaluation of the Hankel transform: Remarks," J. Opt. Soc. Amer., vol. 10, no. 9, pp. 1872-1874, Sept. 1993.
11. O. A. Sharafeddin, H. F. Bowen, D. J. Kouri, and D. K. Huffman, "Numerical evaluation of spherical Bessel transforms via fast Fourier transforms," J. Comput. Phys., vol. 100, pp. 294-296, 1992.
12. S. M. Candel, "Dual algorithms for fast calculation of the Fourier-Bessel transform," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 963-972, Oct. 1981.
13. A. V. Oppenheim, G. V. Frisk, and D. R. Martinez, "An algorithm for the numerical evaluation of the Hankel transform," P roc. IEEE, vol. 66, pp. 264-265, Feb. 1978.
14. _, "Computation of the Hankel transform using projections," J. Acoust. Soc. Amer., vol. 68, no. 2, pp. 523-529, Aug. 1980.
15. E. W. Hansen, "Fast Hankel transform algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 666-671, June 1985.
16. W. E. Higgins and D. C. Munson, "An algorithm for computing general integer-order Hankel transforms," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 86-97, Jan. 1987.
17. Y. J. He, A. Cai, and J. A. Sun, "Real-valued Hankel transform approach to image reconstruction from projections," Electron. Lett., vol. 29, no. 20, pp. 1750-1752, Sept. 1993.
18. V. P. Pauca, B. L. Ellerbroek, N. P. Pitsianis, R. J. Plemmons, and X. Sun, "Performance modeling of adaptive-optics imaging systems using fast Hankel transforms," Proc. SPIE, pp. 339-347, July 1998.
19. I. H. Sneddon, The Use of Integral Transforms. New York: McGraw-Hill, 1972.
20. R. Sasiela, Electromagnetic Waves in Turbulence. New York: Springer, 1994.
21. K. B. Oldham and J. Spanier, The Fractional Calculus. New York: Academic, 1974.
22. N. Engheta, "On the role of fractional calculus in electromagnetic theory," IEEE Antennas Propagat. Mag., vol. 39, pp. 35-16, Aug. 1997.
23. M. Unser and I. Daubechies, "On the approximation power of convolution-based least squares versus interpolation," IEEE Trans. Signal Processing, vol. 45, pp. 1697-1711, July 1997.
24. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes. Cambridge, U.K.: Cambridge Univ. Press, 1992.
25. E. Cavanagh and B. D. Cook, "Numerical evaluation of Hankel transforms via Gaussian-Laguerre polynomial expansions," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, pp. 361-366, Aug. 1979.
26. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. New York: McGraw-Hill, 1953, vol. II.