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Improved bispectrum estimation based on modified group delay

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Abstract

This article proposes an improved estimation method for the bispectrum of a system or signal, by applying the modified group delay (MMGD) in the bispectrum domain. To achieve a higher frequency resolution, the bispectrum is computed in frequency domain and further to reduce the variance preserving the frequency resolution, MMGD is applied in the bispectrum domain. The proposed method due to its better frequency resolution not only properly detects the phase coupled frequencies but also reduces the bispectrum magnitude estimate’s variance significantly compared to that of biperiodogram. Compared to the proposed method, though the windowed bispectrum (WB) provides a better reduction in variance, it is unable to detect the coupled frequencies due to its poor frequency resolution. For an AR process in the presence of noise (SNR = 4 dB), the system magnitude estimate by the proposed method has a 27.63% lower normalized sum sample mean square error (NSSMSE) than that by the WB. Also for a non-minimum phase system in presence of noise (SNR = 7 dB), the phase estimation by the new approach has 8.6% lower NSSMSE than that by WB and also it is marginally better than that obtained by applying MMGD in system group delay domain.

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References

  1. Nikias C.L., Raghuveer M.R.: Bispectrum estimation: a digital signal processing framework. Proc. IEEE 75(7), 869–889 (1987)

    Article  Google Scholar 

  2. Nikias C.L., Petropulu A.P.: Higher order spectral analysis: a non-linear signal processing framework. Prentice-Hall, Englewood Cliffs, NJ (1993)

    Google Scholar 

  3. Nikias C.L., Mendel J.M.: Signal processing with higher order spectra. IEEE Signal Process. Mag. 10(3), 10–37 (1993)

    Article  Google Scholar 

  4. Matsuoka T., Ulrych T.J.: Phase estimation using the bispectrum. Proc. IEEE 72, 1403–1411 (1984)

    Article  Google Scholar 

  5. Benveniste A., Goursat M., Ruget G.: Robust identification of non-minimum phase system: blind adjustment of linear equalizer in data communications. IEEE Trans. Automat. Control AC 25(3), 385–399 (1980)

    Article  MathSciNet  Google Scholar 

  6. Yamani A.: Flaw impulse response estimation in ultrasonic non-destructive evolution using bi-cepstra. NDT&E Int. 40, 57–61 (2007)

    Article  Google Scholar 

  7. Yegnanarayana B., Saikia D.K., Krishnan T.R.: Significance of group delay functions in signal reconstruction from spectral magnitude or phase. IEEE Trans. Acoust. Speech Signal Process. 32(3), 610–623 (1984)

    Article  Google Scholar 

  8. Oppenheim A.V., Hayes M.H., Lim J.S.: Iterative procedures for signal reconstruction from fourier transform phase. Opt. Eng. 21, 122–127 (1982)

    Google Scholar 

  9. Santos M.G., Heaveans A., Balbi A., Borrill J., Ferreira P.G., Hanany S., Jaffe A.H., Lee A.T., Rabii B., Richards P.L., Smoot G.F., Stompor R., Winant C.D., Wu J.H.P.: Multiple methods for estimating the cosmic microwave background with application to the maxima data. Mon. Not. R. Astron. Soc. 341, 623–643 (2003)

    Article  Google Scholar 

  10. Raghuveer M.R., Nikias C.L.: Bispectrum estimation: a parametric approach. IEEE Trans. Acoust. Speech Signal Process. 33(4), 1213–1229 (1985)

    Article  Google Scholar 

  11. Peterunin I., Gleman L.: Novel optimization of bicoherence estimation for fatigue monitoring. Insight 50(3), 133–135 (2008)

    Article  Google Scholar 

  12. Narasimhan S.V., Nandini B., Chaitanya R.: Improved phase estimation based on complete bispectrum and modified group delay. Signal Image Video Process. 2, 261–274 (2008)

    Article  MATH  Google Scholar 

  13. Yegnanarayana B., Murthy H.A.: Significance of group delay functions in spectrum estimation. IEEE Trans. Signal Process. 40(9), 2281–2289 (1992)

    Article  MATH  Google Scholar 

  14. 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 (2001)

  15. Narasimhan S.V., Reddy E.I., Plotkin G.R., Swamy M.N.S.: Bispectrum based mixed phase system identification by AR/ARMA models: AR/ARMA models: a group delay approach. IEEE Trans. Circ. Syst. 39(9), 671–674 (1992)

    Article  MATH  Google Scholar 

  16. Narasimhan S.V., Reddy G.R., Plotkin E.I., Swamy M.N.S.: Estimation by bispectrum: a group delay approach. Signal Process. 27(1), 79–86 (1992)

    Article  Google Scholar 

  17. Holambe R.S., Ray A.K., Basu T.K.: Signal phase recovery using the bispectrum. Signal Process. 55(3), 321–337 (1996)

    Article  MATH  Google Scholar 

  18. Pan R., Nikias C.L.: The complex cepstrum of higher order cumulants and non-minimum phase system identification. IEEE Trans. Acoust. Speech Signal Process. 36(2), 186–204 (1988)

    Article  MATH  Google Scholar 

  19. Klein A., Sauer T., Jedynak A., Skrandies W.: Conventional and wavelet coherence applied to sensory-evoked electrical brain activity. IEEE Trans. Biomed. Eng. 53(2), 266–272 (2006)

    Article  Google Scholar 

  20. Shreyamshakumar, B.K.: Group delay functions for time frequency representation and spectral estimation. M.Tech. thesis, Department of Electronics and Communication Engineering, National Institute of Technology, Karnataka, India (2004)

  21. Sandeep, P.: Group delay and its applications. M.Tech. thesis, Department of Electronics and Communication Engineering, National Institute of Technology, Karnataka, India (2007)

  22. Yegnanarayana B., Raghunathan A.: Representation of images through group delay functions. IEEE Trans. ASSP 35(2), 237–240 (1987)

    Article  Google Scholar 

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Authors and Affiliations

  1. Digital Signal Processing Systems Group, Aerospace Electronics and Systems Division, National Aerospace Laboratories, Bangalore, 560017, India

    Nandini Basumallick & S. V. Narasimhan

  2. Council of Scientific and Industrial Research (CSIR), New Delhi, India

    Nandini Basumallick & S. V. Narasimhan

Authors
  1. Nandini Basumallick
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  2. S. V. Narasimhan
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Correspondence to S. V. Narasimhan.

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Basumallick, N., Narasimhan, S.V. Improved bispectrum estimation based on modified group delay. SIViP 6, 273–286 (2012). https://doi.org/10.1007/s11760-011-0217-9

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  • DOI: https://doi.org/10.1007/s11760-011-0217-9

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