Signal, Image and Video Processing

, Volume 2, Issue 3, pp 261–274 | Cite as

Improved phase estimation based on complete bispectrum and modified group delay

  • S. V. Narasimhan
  • Nandini Basumallick
  • Ratana Chaitanya
Original Paper


In this paper, a new method for extracting the system phase from the bispectrum of the system output has been proposed. This is based on the complete bispectral data computed in the frequency domain and modified group delay. The frequency domain bispectrum computation improves the frequency resolution and the modified group delay reduces the variance preserving the frequency resolution. The use of full bispectral data also reduces the variance as it is used for averaging. For the proposed method at a signal to noise ratio of 5dB, the reduction in root mean square error is in the range of 1.5–7 times over the other methods considered.


Bispectrum Modified group delay Non-minimum phase system identification Phase estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Raghuveer M.R. and Nikias C.L. (1987). Bispectrum estimation: a digital signal processing framework. Proc. IEEE 75(7): 869–89 CrossRefGoogle Scholar
  2. 2.
    Holambe R.S., Ray A.K. and Basu T.K. (1996). Signal phase recovery using the bispectrum. Signal Process. 55: 321–337 MATHCrossRefGoogle Scholar
  3. 3.
    Nikias C.L. and Petropulu A.P. (1993). Higher Order Spectral Analysis: A Non-linear Signal Processing Framework. Signal Processing Series. Prentice-Hall, Englewood Cliffs Google Scholar
  4. 4.
    Narasimhan S.V., Reddy G.R., Plotkin E.I. and Swamy M.N.S. (1992). Phase estimation by bispectrum: A group delay approach. Signal Process. 27(1): 79–86 CrossRefGoogle Scholar
  5. 5.
    Raghuveer M.R. and Nikias C.L. (1985). Bispectrum estimation: A parametric approach. IEEE Trans. Acoust. Speech Signal Process. 33(4): 1213–1229 CrossRefGoogle Scholar
  6. 6.
    Pan R. and Nikias C.L. (1988). The Complex cepstrum of higher order cumulants and non-minimum phase system identification. IEEE Trans. Acoust. Speech Signal Process. 36(2): 186–204 MATHCrossRefGoogle Scholar
  7. 7.
    Narasimhan S.V., Reddy G.R., Plotkin E.I. and Swamy M.N.S. (1992). Bispectrum based mixed phase system identification by AR/ARMA models: AR/ARMA models: a group delay approach. IEEE Trans. Circuits Syst 39(9): 671–674 MATHCrossRefGoogle Scholar
  8. 8.
    Yegnanarayana B., Saikia D.K. and Krishnan T.R. (1984). Significance of group delay functions in signal reconstruction from spectral magnitude or phase. IEEE Trans. ASSP 32(3): 610–623 Google Scholar
  9. 9.
    Nikias, C.L., Mendel, J.M.: Signal processing with higher order spectra. IEEE Signal Process. Mag. pp. 10–37, July (1993)Google Scholar
  10. 10.
    Yegnanarayana B. and Murthy H.A. (1992). Significance of group delay functions in spectrum estimation. IEEE Trans. Signal Process. 40(9): 2281–2289 MATHCrossRefGoogle Scholar
  11. 11.
    Matsuoka T. and Ulrych T.J. (1984). Phase estimation using the bispectrum. Proc. IEEE 72: 1403–1411 CrossRefGoogle Scholar
  12. 12.
    Benveniste, M.G., Ruget, G.: Robust identification of non- minimum phase system: Blind adjustment of linear equalizer in data communications. IEE Trans. Automat. Control, AC-25 (June), pp. 385–398 (1980)Google Scholar
  13. 13.
    Oppenheim A.V., Hayes M.H. and Lim J.S. (1982). Iterative procedures for signal reconstruction from Fourier Transform phase. Opt. Eng. 21(February): 122–127 Google Scholar
  14. 14.
    Subba Rao, T., Gabbar, M.M.: An introduction to bispectral analysis and bilinear time series models. In: Brillinger D.R. et al. (eds.) Lecture Notes on Statistics, vol. 24, Springer, Berlin (1984)Google Scholar
  15. 15.
    Yegnanarayana: Speech analysis by pole-zero decomposition of short time spectra. Signal Process. 17, 141–150 (1989)Google Scholar
  16. 16.
    Yamani: Flaw impulse response estimation in ultrasonic non-destructive evolution using bi-cepstra. NDT&E Int. vol. 40, pp. 57–61 (2007)Google Scholar
  17. 17.
    Hazarathaiah, M., Narasimhan, S.V.: Phase estimation based on bispectrum and modified group delay. In: Signal Processing and Communication (SPCOM 2001), Bangalore, Organized by the IEEE Signal Processing Society, Bangalore ChapterGoogle Scholar
  18. 18.
    Narasimhan S.V. and Giridhar P.V.S. (2000). Improved system blind identification based on second order cyclostatinary statistics: A group delay approach. Academy Proc. Eng. Sci. SADHANA 25(122): 85–96 Google Scholar
  19. 19.
    Narasimhan S.V., Hazarathaiah M. and Giridhar P.V.S. (2005). Channel blind identification based on cyclostationarity and group delay. Signal Process. 85(7): 1275–1286 CrossRefMATHGoogle Scholar
  20. 20.
    Petropulu, A.P., Abeyratne, U.R.: System reconstruction from higher order spectra slices. IEEE Trans. Signal Process. 45(9) (1997)Google Scholar

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  • S. V. Narasimhan
    • 1
  • Nandini Basumallick
    • 1
  • Ratana Chaitanya
    • 2
  1. 1.Aerospace Electronics and Systems DivisionNational Aerospace LaboratoryBangaloreIndia
  2. 2.Department of Electronics and Communication EngineeringNational Institute of TechnologySurathkalIndia

Personalised recommendations