Skip to main content
SpringerLink
Log in

Real-time FFT algorithm applied to on-line spectral analysis

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

On-line running spectral analysis is of considerable interest in many electrophysiological signals, such as the EEG (electroencephalograph). This paper presents a new method of implementing the fast Fourier transform (FFT) algorithm. Our “real-time FFT algorithm” efficiently utilizes computer time to perform the FFT computation while data acquisition proceeds so that local butterfly modules are built using the data points that are already available. The real-time FFT algorithm is developed using the decimation-in-time split-radix FFT (DIT sr-FFT) butterfly structure. In order to demonstate the synchronization ability of the proposed algorithm, the authors develop a method of evaluating the number of arithmetic operations that it requires. Both the derivation and the experimental result show that the real-time FFT algorithm is superior to the conventional whole-block FFT algorithm in synchronizing with the data acquisition process. Given that the FFT sizeN=2r, real-time implementation of the FFT algorithm requires only 2/r the computational time required by the whole-block FFT algorithm.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Barash and Y. Ritov, Logarithmic pruning of FFT frequencies,IEEE Trans. Signal Processling, 41 (3), 1398–1400, 1993.

    Google Scholar 

  2. R. G. Bickford, Computer analysis of background activity, Rémond, A. (ed.),EEG Informatics, Elsevier, Amsterdam, 1977, pp. 215–232.

    Google Scholar 

  3. V. Boriakoff, FFT computation with systolic arrays: A new architecture,IEEE Trans. Circuits Systems — II: Analog Digital Signal Process., 41(4), 278–284, 1994.

    Google Scholar 

  4. J. W. Cooley and J. W. Tukey, An algorithm for machine computation of complex Fourier series,Math. Comp., 19, 297–301, 1965.

    Google Scholar 

  5. R. Cooper, J. W. Osselton, and J. C. Shaw,EEG Technology, 3rd ed., Butterworth, Woburn, MA, 1980, Chapter 6.

    Google Scholar 

  6. P. Duhamel, Implementation of “split-radix” FFT algorithms for complex, real and real-symmetric data,IEEE Trans. Acoust. Speech Signal Process., ASSP-34, 285–295, 1986.

    Google Scholar 

  7. P. Duhamel and H. Hollmann, Split radix FFT algorithm,Electronics Lett., 20(1), 14–16, 1984.

    Google Scholar 

  8. A. Gevins, P. Brickett, B. Costales, J. Le, and B. Reutter, Beyond topographic mapping: Towards functional-anatomical imaging with 124-channel EEGs and 3-D MRIs,Brain Topography, 3, 53–64, 1990.

    Google Scholar 

  9. P. C. Lo and Y. Y. Lee, Real-time implementation of the split-radix FFT—An algorithm to efficiently construct local butterfly modules,Signal Processing, submitted.

  10. J. D. Markel, FFT pruning,IEEE Trans. Audio Electroacoust., AU-19(4), 305–311, 1971.

    Google Scholar 

  11. K. Nagai, Pruning the decimation-in-time FFT algorithm with frequency shift,IEEE Trans. Acoust. Speech Signal Process., ASSP-34(4), 1008–1010, 1986.

    Google Scholar 

  12. A. V. Oppenheim and R. W. Schafer,Discrete-Time Signal processing, Prentice-Hall, Englewood Cliffs, NJ, 1989, Chapter 9.

    Google Scholar 

  13. D. E. Panera, S. R. Mani, and S. H. Nawab, STFT computation using pruned FFT algorithms,IEEE Signal Processing Lett., 1(4), 61–63, 1994.

    Google Scholar 

  14. C. Roche, A split-radix partial input/output fast Fourier transform algorithm,IEEE Trans. Signal Process., 40(5), 1273–1276, 1992.

    Google Scholar 

  15. I. W. Selesnick and C. S. Burrus, Automatic generation of prime length FFT programs,IEEE Trans. Signal Process., 44(1), 14–24, 1996.

    Google Scholar 

  16. A. N. Skodras, Effecient computation of the split-radix FFT,IEEE Proceedings—F, 139(1), 56–60, 1992.

    Google Scholar 

  17. H. V. Sorensen and C. S. Burrus, Efficient computation of the DFT with only a subset of input or output points,IEEE Trans. Signal Process., 41(3), 1184–1200, 1993.

    Google Scholar 

  18. H. V. Sorensen, M. T. Heideman, and C. S. Burrus, On computing the split-radix FFT,IEEE Trans. Acoust. Speech Signal Process., ASSP-34(1), 152–156, 1986.

    Google Scholar 

  19. T. V. Sreenivas and P. V. S. Rao, High resolution narrow-band spectra by FFT pruning,IEEE Trans. Acoust. Speech Signal Process., ASSP-28(2), 254–257, 1980.

    Google Scholar 

  20. P. R. Uniyal, Transforming real-valued sequences: Fast Fourier versus fast Hartley transform algorithms,IEEE Trans. Signal Process., 42(11), 3249–3254, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Control Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, 30050, Hsinchu, Taiwan, Republic of China

    Pei-Chen Lo & Yu-Yun Lee

Authors
  1. Pei-Chen Lo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu-Yun Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the National Science Council of Taiwan, Republic of China, under grant NSC87-2213-E-009-128.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lo, PC., Lee, YY. Real-time FFT algorithm applied to on-line spectral analysis. Circuits Systems and Signal Process 18, 377–393 (1999). https://doi.org/10.1007/BF01200789

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01200789

Keywords

Search

Navigation