Journal of Applied Mathematics

Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions

Huaiqing Zhang, Yu Chen, and Xin Nie

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The Pravin method for Hankel transforms is based on the decomposition of kernel function with exponential function. The defect of such method is the difficulty in its parameters determination and lack of adaptability to kernel function especially using monotonically decreasing functions to approximate the convex ones. This thesis proposed an improved scheme by adding new base function in interpolation procedure. The improved method maintains the merit of Pravin method which can convert the Hankel integral to algebraic calculation. The simulation results reveal that the improved method has high precision, high efficiency, and good adaptability to kernel function. It can be applied to zero-order and first-order Hankel transforms.

Article information

J. Appl. Math., Volume 2014 (2014), Article ID 105469, 7 pages.

First available in Project Euclid: 2 March 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Zhang, Huaiqing; Chen, Yu; Nie, Xin. Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions. J. Appl. Math. 2014 (2014), Article ID 105469, 7 pages. doi:10.1155/2014/105469.

Export citation


  • V. K. Singh, R. K. Pandey, and S. Singh, “A stable algorithm for Hankel transforms using hybrid of Block-pulse and Legendre polynomials,” Computer Physics Communications, vol. 181, no. 1, pp. 1–10, 2010.
  • A. E. Siegman, “Quasi fast Hankel transforms,” Optics Letters, vol. 1, pp. 13–15, 1977.
  • V. K. Singh, O. P. Singh, and R. K. Pandey, “Numerical evaluation of the Hankel transform by using linear Legendre multi-wavelets,” Computer Physics Communications, vol. 179, no. 6, pp. 424–429, 2008.
  • A. V. Oppenheim, G. V. Frisk, and D. R. Martinez, “Computation of the Hankel transform using projections,” The Journal of the Acoustical Society of America, vol. 68, no. 2, pp. 523–529, 1980.
  • L. Knockaert, “Fast Hankel transform by fast sine and cosine transforms: the Mellin connection,” IEEE Transactions on Signal Processing, vol. 48, no. 6, pp. 1695–1701, 2000.
  • R. Barakat and E. Parshall, “Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy,” Applied Mathematics Letters, vol. 9, no. 5, pp. 21–26, 1996.
  • L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, “Quasi-discrete Hankel transform,” Optics Letters, vol. 23, no. 6, pp. 409–411, 1998.
  • M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” Journal of the Optical Society of America A: Optics and Image Science, and Vision, vol. 21, no. 1, pp. 53–58, 2004.
  • E. B. Postnikov, “About calculation of the Hankel transform using preliminary wavelet transform,” Journal of Applied Mathematics, vol. 2003, no. 6, pp. 319–325, 2003.
  • P. S. Zykov and E. B. Postnikov, “Application of the wavelet transform with a piecewise linear basis to the evaluation of the Hankel transform,” Computational Mathematics and Mathematical Physics, vol. 44, no. 3, pp. 396–400, 2004.
  • V. K. Singh, O. P. Singh, and R. K. Pandey, “Efficient algorithms to compute Hankel transforms using wavelets,” Computer Physics Communications, vol. 179, no. 11, pp. 812–818, 2008.
  • R. K. Pandey, V. K. Singh, and O. P. Singh, “An improved method for computing Hankel transform,” Journal of the Franklin Institute, vol. 346, no. 2, pp. 102–111, 2009.
  • P. K. Gupta, S. Niwas, and N. Chaudhary, “Fast computation of Hankel transform using orthonormal exponential approximation of complex kernel function,” Journal of Earth System Science, vol. 115, no. 3, pp. 267–276, 2006.
  • L. Gr. Ixaru and G. Vanden Berghe, Exponential Fitting, vol. 568 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004.
  • W. L. Anderson, “Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering,” Geophysics, vol. 44, no. 7, pp. 1287–1305, 1979. \endinput