Chinese Science Bulletin

, Volume 52, Issue 17, pp 2438–2442 | Cite as

RETRACTED ARTICLE: A non-commutative time-frequency tomography

  • Liu JianCai Email author
  • Xu JiaKai 
  • Ning XinBao 
  • Tian Run 
Articles Acoustics


The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N).


time-frequency non-commuting tomography marginal distribution 


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Copyright information

© Science in China Press 2007

Authors and Affiliations

  • Liu JianCai 
    • 1
    Email author
  • Xu JiaKai 
    • 1
  • Ning XinBao 
    • 1
  • Tian Run 
    • 1
  1. 1.Key Laboratory of Modern Acoustics, Department of Electronics Science and Engineering; Institute of Biological Medical Electronic EngineeringNanjing UniversityNanjingChina

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