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Computing Deblurred Time-Frequency Distributions Using Artificial Neural Networks

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Abstract

This paper presents an effective correlation vectored taxonomy algorithm to compute highly concentrated time-frequency distributions (TFDs) using localized neural networks (LNNs). Spectrograms and pre-processed Wigner–Ville distributions of known signals are vectorized and clustered as per the elbow criterion to constitute the training data for multiple artificial neural networks. The best trained networks become part of the LNNs. Test TFDs of unknown signals are then processed through the algorithm and presented to the LNNs. Experimental results demonstrate that appropriately vectored and clustered data once processed through the LNNs produce high resolution TFDs. Examples are presented to show the effectiveness of the proposed algorithm via analysis based on entropy and visual interpretation.

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References

  1. Ahmad, J., Shafi, I., Shah, S.I., Kashif, F.M., Analysis and Comparison of Neural Network Training Algorithms for the Joint Time-Frequency Analysis, Proc. IASTED Intl. Conf. on Artificial Intelligence and Applications, pp. 193–198, Austria, Feb. 2006.

  2. Akan, A., Signal-Adaptive Evolutionary Spectral Analysis Using Instantaneous Frequency Estimation, FREQUENZ Journal of RF-Engineering and Telecommunications, Vol. 59, No. 7–8/2005, pp. 201–205, 2005.

    Google Scholar 

  3. Akan, A., Chaparro, L.F., Evolutionary Chirp Representation of Non-stationary Signals via Gabor Transform, Signal Processing, Vol. 81, No. 11, pp. 2429–2436, 2001.

    Article  MATH  Google Scholar 

  4. Baraniuk, R.G., Jones, D.L., Signal-Dependent Time-Frequency Analysis Using a Radially Gaussian Kernel, IEEE Trans. Signal Processing, Vol. 32, pp. 263–284, 1993.

    MATH  Google Scholar 

  5. Barbarossa, S., Analysis of Multicomponent LFM Signals by a Combined Wigner–Hough Transform, IEEE Trans. Signal Processing, Vol. 46, No. 6, pp. 1511–1515, 1995.

    Article  Google Scholar 

  6. Barkat, B., Abed-Meraim, K., Algorithms for Blind Components Separation and Extraction from the Time-Frequency Distribution of Their Mixture, EURASIP Journal on Applied Signal Processing, Vol. 2004, No. 13, pp. 2025–2033, 2004.

    Article  Google Scholar 

  7. Basu, M., Su, M., Deblurring Images Using Projection Pursuit Learning Network, IEEE Trans. Signal Processing, 1999.

  8. Boashash, B., Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier, Oxford, UK, 769 pages, 2003.

    Google Scholar 

  9. Chaparro, L.F., Suleesathira, R., Akan, A., Unsal, B., Instantaneous Frequency Estimation Using Discrete Evolutionary Transform for Jammer Excision, Proc. ICASSP ’01, Vol. 6, pp. 3525–3528, 7–11 May 2001.

    Google Scholar 

  10. Chauvin, Y., Rumelhart, D.E., Back Propagation: Theory, Architecture, and Applications, Lawrence Erlbaum Associates, Hillsdale, NJ, 1995.

    Google Scholar 

  11. Cohen, L., Time Frequency Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1995.

    Google Scholar 

  12. Emresoy, M.K., Loughlin, P.J., Weighted Least Square Cohen-Posch Time-Frequency Distribution Functions, IEEE Trans. Signal Processing, Vol. 46, No. 3, pp. 753–757, 1998.

    Article  Google Scholar 

  13. Gray, R.M., Entropy and Information Theory, Springer, New York, 1990.

    MATH  Google Scholar 

  14. Groutage, D., A Fast Algorithm for Computing Minimum Cross-Entropy Positive Time-Frequency Distributions, IEEE Trans. Signal Processing, Vol. 45, No. 8, pp. 1954–1970, 1997.

    Article  Google Scholar 

  15. Hagan, M.T., Demuth, H.B., Beale, M., Neural Network Design, Thomson Learning USA, Boston, MA, 1996.

    Google Scholar 

  16. LJubisa, S., Vladimir, K., Algorithm for the Instantaneous Frequency Estimation Using Time-Frequency Distributions with Adaptive Window Width, IEEE Signal Processing Letters, Vol. 5, No. 9, pp. 224–227, 1998.

    Article  Google Scholar 

  17. MacKay, D.J.C., A Practical Bayesian Framework for Back Propagation Network, Neural Computation, Vol. 4, No. 3, pp. 448–472, 1992.

    Article  Google Scholar 

  18. Pitton, J.W., Positive Time-Frequency Distributions via Quadratic Programming, Journal of Multidimensional Systems and Signal Processing, Vol. 9, No. 4, pp. 439–445, 1998.

    Article  MATH  Google Scholar 

  19. Pitton, J., Loughlin, P., Atlas, L., Positive Time-Frequency Distributions via Maximum Entropy Deconvolution of the Evolutionary Spectrum, Proc. ICASSP ‘93, Vol. IV, pp. 436–439, 1993.

    Google Scholar 

  20. Shafi, I., Ahmad, J., Shah, S.I., Kashif, F.M., Impact of Varying Neurons and Hidden Layers in Neural Network Architecture for a Time Frequency Application, Proc. 10th IEEE Intl. Multi Topic Conf., INMIC 2006, Islamabad, Pakistan, 23–24 Dec. 2006.

  21. Shah, S.I., Loughlin, P.J., Chaparro, L.F., El-Jaroudi, A., Informative Priors for Minimum Cross-Entropy Positive Time Frequency Distributions, IEEE Signal Processing Letters, Vol. 4, No. 6, pp. 176–177, 1997.

    Article  Google Scholar 

  22. Slueesathira, R., Chaparro, L.F., Akan, A., Discrete Evolutionary Transform for Positive Time Frequency Signal Analysis, Journal of Franklin Institute, Vol. 337, No. 4, pp. 347–364, 2000.

    Article  Google Scholar 

  23. Stankovic, L., Highly Concentrated Time-Frequency Distributions: Pseudo Quantum Signal Representation, IEEE Trans. Signal Processing, Vol. 45, No. 3, pp. 543–551, 1997.

    Article  MathSciNet  Google Scholar 

  24. Suleesathira, R., Chaparro, L.F., Interference Mitigation in Spread Spectrum Using Discrete Evolutionary and Hough Transforms, Proc. ICASSP ’00, Vol. 5, pp. 2821–2824, 5–9 June 2000.

    Google Scholar 

  25. Yagle, A.E., Torres-Fernandez, J.E., Construction of Signal-Dependent Cohen’s-class time-frequency distributions using iterative blind deconvolution, Proc. SPIE, Advanced Signal Processing Algorithms, Architectures, and Implementations XIII. Edited by Luk, Franklin T., Vol. 5205, pp. 47–58, 2003.

  26. http://www-dsp.rice.edu.

  27. http://en.wikipedia.org/wiki/Data_clustering.

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Authors and Affiliations

  1. Center for Advanced Studies in Engineering (C@SE), 19-Ataturk Avenue, G-5/1, Islamabad, Pakistan

    Imran Shafi

  2. Iqra University, Islamabad Campus, Sector H-9, Islamabad, Pakistan

    Jamil Ahmad & Syed Ismail Shah

  3. Laboratory for Electromagnetic and Electronic Systems (LEES), Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Faisal M. Kashif

Authors
  1. Imran Shafi
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  2. Jamil Ahmad
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  3. Syed Ismail Shah
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  4. Faisal M. Kashif
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Corresponding author

Correspondence to Imran Shafi.

Additional information

This work was supported by the Higher Education Commission (HEC) of Pakistan under the 200 Merit Scholarship Scheme.

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Shafi, I., Ahmad, J., Shah, S.I. et al. Computing Deblurred Time-Frequency Distributions Using Artificial Neural Networks. Circuits Syst Signal Process 27, 277–294 (2008). https://doi.org/10.1007/s00034-008-9027-x

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  • DOI: https://doi.org/10.1007/s00034-008-9027-x

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