, Volume 23, Issue 1, pp 57–71 | Cite as

Power spectrum estimation of complex signals and its application to Wigner-Ville distribution: A group delay approach

  • S V Narasimhan
  • E I Plotkin
  • M N S Swamy
Recent Results In Signal Processing And Communications


In this paper, a method of estimating the power spectrum of a complex signal based on the Group Delay function (GD) is proposed and also applied to the Wigner-Ville Distribution (WVD) to reduce the ripple effect due to the truncation of the autocorrelation sequence. The proposed method is realised by the GD for a complex signal and the modified GD concept. This extends the performance advantages of the modified GD applicable to a real signal, to a complex one. Further, its application to WVD, reduces the truncation/ripple effect without sacrificing any frequency resolution, as nocommon window function is used. Significant improvement in performance, in terms of reduction in variance without any compromise on resolution and higher noise immunity, has been found over those of the periodogram and windowed WVD.


Complex signals power spectrum estimation group delay approach Wigner-Ville distribution Gibb’s ripple effect 


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  1. Cohen L 1989 Time-frequency distribution — A review.Proc. IEEE. 77: 941–981CrossRefGoogle Scholar
  2. Flandrin P 1984 Some features of time-frequency representation of multicomponent signals.Int. Conf. on Acoustics, Speech and Signal Processing, pp 41B.4.1–41B.4.4Google Scholar
  3. Jeong J, Williams W J 1992 Kernel design with reduced interference distributions.IEEE Trans. Signal Process. 38: 402–412CrossRefGoogle Scholar
  4. Kay S M 1988Modern spectral estimation: Theory and application (Englewood Cliffs, NJ: Prentice Hall)MATHGoogle Scholar
  5. Murthy H A, Yegnanarayana B 1991 Speech processing using group delay function.Signal Process. 22: 259–267CrossRefGoogle Scholar
  6. Picone J 1988 Spectrum estimation using an analytic signal representation.Signal Process. 15: 169–182CrossRefMathSciNetGoogle Scholar
  7. Reddy G R, Rao V V 1987 Group delay functions for complex signals.Signal Process. 12: 5–15CrossRefGoogle Scholar
  8. Velez E F, Absher R G 1990 Spectral estimation based on the Wigner-Ville representation.Signal Process. 20: 325–346MATHCrossRefGoogle Scholar
  9. Yegnanarayana B, Murthy H A 1992 Significance of group delay functions in spectrum estimation.IEEE Trans. Signal Process. 40: 2281–2289MATHCrossRefGoogle Scholar
  10. Yegnanarayana B, Saikia D K, Krishnan T R 1984 Significance of group delay functions in signal reconstruction from spectral magnitude or phase.IEEE Trans. Acoustics, Speech Signal Process. ASSP-32: 610–623CrossRefGoogle Scholar

Copyright information

© the Indian Academy of Sciences 1998

Authors and Affiliations

  • S V Narasimhan
  • E I Plotkin
    • 1
  • M N S Swamy
    • 2
  1. 1.Centre for Communication and Signal Processing, Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada
  2. 2.Aerospace Electronics DivisionNational Aerospace LabsBangaloreIndia

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