Skip to main content
SpringerLink
Log in

A Keystone-Based Cosine Transform

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper introduces a new time-frequency transform, referred to as the keystone-based cosine transform (KCT), to process real-valued multi-component linear frequency-modulated signals. Theoretical derivation shows that the KCT is a bilinear-based transform, but has a property of asymptotic linearity with negligible cross-terms. It also has high signal energy concentration. Experimental simulations show that compared with fractional cosine transform, the KCT can provide better performance on the distribution concentration and noisy signal detection.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Y. Chen, C. Clamente, J. Soraghan, S. Weiss, Fractional cosine transform (FRCT)-turbo based OFDM for underwater acoustic communication. In: 2015 Sensor Signal Processing for Defence (SSPD) (2015), pp. 1–5

  2. L. Cohen, Time-frequency distributions: a review. Proc. IEEE 77(7), 941–981 (1989)

    Article  Google Scholar 

  3. L. Cohen, Time-Frequency Analysis (Prentice Hall, New Jersey, 1995)

    Google Scholar 

  4. L. Cohen, P. Loughlin, leid1. Time-frequency analysis: theory and applications. J. Acoust. Soc. Am. 134(5), 4002 (2013)

    Article  Google Scholar 

  5. S. Luo, G. Bi, X. Lv, F. Hu, Performance analysis on Lv distribution and its application. Digit. Signal Proc. 23(3), 797–807 (2013)

    Article  MathSciNet  Google Scholar 

  6. S. Luo, X. Li, G. Bi, Short-time Lv transform and its application for non-linear FM signal detection. J. Syst. Eng. Electron. 26(6), 1159–1168 (2015)

    Article  Google Scholar 

  7. S. Luo, X. Li, S. Li, G. Bi, Adaptive interference suppression based on Lv distribution for DSSS communications. J. Circuits Syst. Comput. 24(1), 1–27 (2015)

    Article  Google Scholar 

  8. X. Lv, G. Bi, C. Wan, M. Xing, Lv’s distribution: principle, implementation, properties and performance. IEEE Trans. Signal Process. 59(8), 3576–3591 (2011)

    Article  MathSciNet  Google Scholar 

  9. X. Lv, M. Xing, S. Zhang, Z. Bao, Keystone transformation of the Wigner–Ville distribution for analysis of multicomponent LFM signals. Signal Process. 89(5), 791–806 (2009)

    Article  MATH  Google Scholar 

  10. A. Papoulis, Systems and Transforms with Application in Optics (McGraw-Hill, New York, 1968), pp. 203–204

    Google Scholar 

  11. S.C. Pei, J.J. Ding, Fractional cosine, sine, and Hartley transforms. IEEE Trans. Signal Process. 50(7), 1661–1680 (2002)

    Article  MathSciNet  Google Scholar 

  12. N. Roma, L. Sousa, A tutorial overview on the properties of the discrete cosine transform for encoded image and video processing. Signal Process. 91(11), 2443–2464 (2011)

    Article  MATH  Google Scholar 

  13. E. Sejdic, I. Djurovic, L. Stankovic, Fractional Fourier transform as a signal processing tool: an overview of recent developments. Signal Process. 91(6), 1351–1369 (2011)

    Article  MATH  Google Scholar 

  14. B. Shekar, G. Thippeswamy, M. Kumari, Face recognition based on fractional discrete cosine transform. In: 2011 International Conference on Recent Trends in Information Technology (ICRTIT) (2011), pp. 987–991

  15. L. Stankovic, A method for time-frequency analysis. IEEE Trans. Signal Process. 42(1), 225–229 (1994)

    Article  Google Scholar 

  16. J. Wood, D. Barry, Radon transformation of time-frequency distributions for analysis of multicomponent signals. IEEE Trans. Signal Process. 42(11), 3166–3177 (1994)

    Article  Google Scholar 

  17. P. Yip, The Transforms and Applications Handbook—Chapter 3: Sine and Cosine Transforms (CRC Press LLC, Boca Raton, 2000)

    Google Scholar 

  18. D. Zhu, Y. Li, Z. Zhu, A keystone transform without interpolation for SAR ground moving-target imaging. IEEE Geosci. Remote Sens. Lett. 4(1), 18–22 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, People’s Republic of China

    Shan Luo

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Guoan Bi

  3. Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ, USA

    Yong Xiao

  4. School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, People’s Republic of China

    Rongping Lin

Authors
  1. Shan Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoan Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rongping Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shan Luo.

Additional information

This work was supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry [2015] 1098, the National Natural Science Foundation of China (NSFC) (61401070), and the Fundamental Research Funds for the Central Universities (ZYGX2014J097).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, S., Bi, G., Xiao, Y. et al. A Keystone-Based Cosine Transform. Circuits Syst Signal Process 36, 3438–3447 (2017). https://doi.org/10.1007/s00034-016-0457-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-016-0457-6

Keywords

Search

Navigation