Skip to main content
SpringerLink
Log in

RETRACTED ARTICLE: A non-commutative time-frequency tomography

  • Articles
  • Acoustics
  • Published:
Chinese Science Bulletin

Abstract

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).

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. Boudreaux-Bartels G F. Mixed time-frequency signal transformations. In: Poularikas A D, ed. The Transforms and Applications Handbook, Alabama: CRC Press, 1996, 887–962

    Google Scholar 

  2. Wood J C, Barry D T. Linear signal synthesis using the Radon-Wigner transform. IEEE Trans Signal Process, 1994, 42: 2105–2111

    Article  ADS  Google Scholar 

  3. Zhang F, Bi G, Chen Y Q. Tomography time-frequency transform. IEEE Trans Signal Process, 2002, 50: 1289–1297

    Article  MathSciNet  ADS  Google Scholar 

  4. Lohmann A W, Soffer B H. Relationships between the Radon-Wigner and fractional Fourier transforms. J Opt Soc Amer A, 1994, 11(6): 1798–1801

    Article  MathSciNet  ADS  Google Scholar 

  5. Syed Ismail Shah, Amro El-Jaroudi, Patrick J. Loughlin, et al. Signal synthesis and positive time-frequency distributions. J Franklin Institute, 2000, 37: 317–328

    Article  Google Scholar 

  6. Carlen E, Mendes R V. Non-commutative space-time and the uncertainty principle. Phy Lett A, 2001, 290: 109–114

    Article  MathSciNet  CAS  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Modern Acoustics, Department of Electronics Science and Engineering; Institute of Biological Medical Electronic Engineering, Nanjing University, Nanjing, 210093, China

    Liu JianCai, Xu JiaKai, Ning XinBao & Tian Run

Authors
  1. Liu JianCai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xu JiaKai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ning XinBao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tian Run
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liu JianCai.

Additional information

Supported by the Open Project of the Key Laboratory of Jiangsu Province (Grant No. KJS03078)

This article will be retracted by Science Bulletin (formerly known as Chinese Science Bulletin) as per the Committee on Publication Ethics (COPE) guidelines. The retraction is after thorough investigation which has been found that the content is partially plagiarized from the article previously published: Man'ko V I, Vilela Mendes R. Non-commutative time-frequency tomography. Phys Lett A, 1999, 263: 53-61

The online version of the original article can be found at http://engine.scichina.com/publisher/scp/journal/Sci%20Bull%20Chin/52/17/10.1007/s11434-007-0367-x?slug=abstract

An erratum to this article can be found at https://doi.org/10.1016/j.scib.2019.01.003

About this article

Cite this article

Liu, J., Xu, J., Ning, X. et al. RETRACTED ARTICLE: A non-commutative time-frequency tomography. CHINESE SCI BULL 52, 2438–2442 (2007). https://doi.org/10.1007/s11434-007-0367-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11434-007-0367-x

Keywords

Search

Navigation