Skip to main content
SpringerLink
Log in

Fast Fourier Transform on Hexagons

  • Conference paper
Current Trends in High Performance Computing and Its Applications

Summary

We propose fast algorithms for computing the discrete Fourier transforms on hexagon. These algorithms are easy to implement, they reduce the computation complexity from \(\mathcal{O}\)(M 2) to \(\mathcal{O}\)(M log M), where M is the total number of sampling points.

This project is supported by National Natural Science Foundation of China (No. 60173021) and Basic Research Foundation of ISCAS (No. CXK35281).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. W. Cooley and J. W. Tukey. An algorithm for the machine calculation of complex Fourier series. Math. Comp., 19:297–301, 1965.

    MathSciNet  MATH  Google Scholar 

  2. D. E. Dudgeon and R. M. Mersereau. Mutlidimensional Digital Signal Processing. Prentice-Hall: Englewood Cliffs, NJ, 1984.

    Google Scholar 

  3. R. M. Mersereau. The processing of hexagonally sampled two-dimensional signals. Proc. IEEE, 67:930–949, 1979.

    Article  Google Scholar 

  4. R. M. Mersereau and T. C. Speake. Unifed treatment of Cooley-Tukey algorithms for the evaluation of multidimensional DFT. IEEE Transactions on Acoustic, Speech and Signal Processing, 29:1011–1018, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. M. Mersereau and T. C. Speake. The processing of periodically sampled multidimensional signals. IEEE Transactions on Acoustic, Speech and Signal Processing, 31:188–194, 1983.

    Article  MATH  Google Scholar 

  6. D. N. Rockmore. The FFT: An algorithm the whole family can use. Computing in Science & Engineering, 2(1):60–64, 2000.

    Article  MathSciNet  Google Scholar 

  7. J. Sun. Generalized Fourier transformation in an arbitrary triangular domain. Advances in Computational Mathematics, to appear.

    Google Scholar 

  8. J. Sun. Multivariate Fourier series over a class of non tensor-product partition domains. J. Comput. Math., 21:53–62, 2003.

    MATH  MathSciNet  Google Scholar 

  9. P.N. Swarztrauber. Vectorizing the ffts. In G. Rodrigue, editor, Parallel Computations, pages 51–83. Academic Press, 1982.

    Google Scholar 

  10. J. L. Zapata and G. X. Ritter. Fast fourier transform for hexagonal aggregates. Journal of Mathematical Imaging and Vision, 12:183–197, 2000.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Parallel Computing, Institute of Software, Chinese Academy of Sciences, Beijing, 100080, People’s Rrepublic of China

    Huiyuan Li & Jiachang Sun

Authors
  1. Huiyuan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiachang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, 200072, Shanghai, People’s Republic of China

    Wu Zhang  & Weiqin Tong  & 

  2. Department of Mathematics, Southern Methodist University, 75275-0156, Dallas, TX, USA

    Zhangxin Chen

  3. Department of Mathematics, University of Houston, 77204-3476, Houston, TX, USA

    Roland Glowinski

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, H., Sun, J. (2005). Fast Fourier Transform on Hexagons. In: Zhang, W., Tong, W., Chen, Z., Glowinski, R. (eds) Current Trends in High Performance Computing and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27912-1_44

Download citation

Publish with us

Policies and ethics

Search

Navigation