access icon free Reconstruction and basis function construction of electromagnetic interference source signals based on Toeplitz-based singular value decomposition

© The Institution of Engineering and Technology
Received 29/05/2016, Accepted 28/07/2016, Published 03/08/2016

In this study, the authors propose a novel method, namely Toeplitz-based singular value decomposition (or TL-SVD for short) for the reconstruction and basis function construction of electromagnetic interference (EMI) source signals. Given a specific EMI source signal, they first construct a Toeplitz type data matrix. By applying singular value decomposition (SVD) to the constructed matrix, they obtain a set of singular values, which are further divided into two parts, corresponding to the clear and noisy components of input signals, respectively. The de-noised signal can then be reconstructed by reserving relatively larger singular values and abandoning smaller ones. Finally, by utilising the compositions of certain vectors resulting from the previous SVD step, the basis function can be constructed. To evaluate the performance of the proposed method, they conduct extensive experiments on both the synthetic data and real EMI signals, by comparing with several state-of-the-art signal reconstruction methods, such as discrete wavelet transform, EEMD, sparse representation based on K-SVD and OMP. Experimental results demonstrate that the proposed method can outperform comparison approaches.

Inspec keywords: signal reconstruction; discrete wavelet transforms; matrix algebra; electromagnetic interference; singular value decomposition

Other keywords: OMP; discrete wavelet transform; Toeplitz-based singular value decomposition; K-SVD; sparse representation; TL-SVD; Toeplitz type data matrix; signal reconstruction; electromagnetic interference source signals; signal basis function construction; EMI source signals; signal denoising; EEMD

Subjects: Algebra; Signal processing and detection; Integral transforms; Digital signal processing; Integral transforms; Algebra; Electromagnetic compatibility and interference

References

    1. 1)
      • 20. Vallet, P., Loubaton, P.: ‘Toeplitz rectification and DOA estimation with music’. IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), 2014, 2014, pp. 2237–2241.
    2. 2)
      • 3. Zhao, D., Lu, H., Li, H.: ‘An ICA and AIS based method for electromagnetic compatibility analysis’, Adv. Mater. Res., 2013, 846-847, pp. 547–550.
    3. 3)
      • 13. Chen, J., Zhang, Z., Wang, Y.: ‘Relevance metric learning for person re-identification by exploiting list wise similarities’, IEEE Trans. Image Process., 2015, 24, (12), pp. 1657–1662.
    4. 4)
      • 21. Ma, H.G., Jiang, Q.B., Liu, Z.Q., et al: ‘A novel blind source separation method for single-channel signal’, Signal Process., 2010, 90, (12), pp. 3232–3241.
    5. 5)
      • 6. Frangakis, A.S., Stoschek, A., Hegerl, R.: ‘Wavelet transform filtering and nonlinear anisotropic diffusion assessed for signal reconstruction performance on multidimensional biomedical data’, IEEE Trans. Biomed. Eng., 2001, 48, (2), pp. 213–222.
    6. 6)
      • 14. Chen, J., Wang, Y., Tang, Y.Y.: ‘Person re-identification by exploiting spatio-temporal cues and multi-view metric learning’, IEEE Signal Process. Lett., 2016, 23, (7), pp. 998–1002.
    7. 7)
      • 16. Zhao, X., Ye, B., Chen, T.: ‘Influence of matrix creation way on signal processing effect of singular value decomposition’ (Journal of South China University of Technology, 2008).
    8. 8)
      • 10. Wang, C., Li, H., Xiang, W., et al: ‘A new signal classification method based on EEMD and FCM and its application in bearing fault diagnosis’, Appl. Mech. Mater., 2014, 602-605, pp. 1803–1806.
    9. 9)
      • 4. Li, H., Wang, C., Zhao, D.: ‘An improved EMD and its applications to find the basis functions of EMI signals’, Math. Probl. Eng., 2015, 2015, pp. 1–8Article ID 150127.
    10. 10)
      • 25. Lu, J., Zhao, Y.: ‘Dominant singular value decomposition representation for face recognition’, Signal Process., 2010, 90, (6), pp. 2087–2093.
    11. 11)
      • 1. Salameh, M.S.A., Zuraiqi, E.T.A.: ‘Solutions to electromagnetic compatibility problems using artificial neural networks representation of vector finite element method’, IET Microw. Antennas Propag., 2008, 2, (4), pp. 348–357.
    12. 12)
      • 23. Tanaka, T., Ueda, K., Satou, K.: ‘A novel detection method of active and reactive currents in single-phase circuits using the correlation and cross-correlation coefficients and its applications’. Industry Applications Conf., 2004. 39th IAS Annual Meeting. Conf. Record of the 2004 IEEE, 2004, vol. l.2, pp. 836–842.
    13. 13)
      • 8. Prince, A., Senroy, N., Balasubramanian, R.: ‘Targeted approach to apply masking signal-based empirical mode decomposition for mode identification from dynamic power system wide area measurement signal data’, IET Gener. Transm. Distrib., 2011, 5, (10), pp. 1025–1032.
    14. 14)
      • 17. Wang, Q., Wang, W., Liu, Z.: ‘Analysis of electromagnetic scattering by using modified characteristic basis function method’, Syst. Eng. Electron., 2010, 32, (10), pp. 2103–2106.
    15. 15)
      • 24. Najafipour, A., Babaee, A., Shahrtash, S.M.: ‘Comparing the trustworthiness of signal-to-noise ratio and peak signal-to-noise ratio in processing noisy partial discharge signals’, IET Sci. Measure. Technol., 2013, 7, (2), pp. 112–118.
    16. 16)
      • 5. Masselos, K., Andreopoulos, Y., Stouraitis, T.: ‘Performance comparison of two-dimensional discrete wavelet transform computation schedules on a VLIW digital signal processor’. IEE Proc. - Vision Image and Signal Processing, 2006, vol. 153, no. 2, pp. 173–180.
    17. 17)
      • 15. Zhao, D., Li, H.: ‘On the computation of inverses and determinants of a kind of special matrices’, Appl. Math. Comput., 2010, 250, pp. 721–726.
    18. 18)
      • 7. Kadambe, S., Srinivasan, P.: ‘Adaptive wavelets for signal classification and compression’, AEU – Int. J. Electron. Commun., 2006, 60, (1), pp. 45–55.
    19. 19)
      • 26. Andrzejak, R.G., Schindler, K., Rummel, C.: ‘Nonrandomness, nonlinear dependence, and nonstationary of electroencephalographic recordings from epilepsy patients’, Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 2012, 86, (4), pp. 2745–2756.
    20. 20)
      • 2. Li, H.Y., Fu, Y., Zhao, D.: ‘Identification of power quality disturbances based on FFT and attribute weighted artificial immune evolutionary classifier’, Appl. Mech. Mater., 2014, 530-531, pp. 277–280.
    21. 21)
      • 11. Aharon, M., Elad, M., Bruckstein, A.K.: ‘K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation’, IEEE Trans. Signal Process., 2006, 54, (11), pp. 4311–4322.
    22. 22)
      • 19. Kakarala, R., Ogunbona, P.O.: ‘Signal analysis using a multiresolution form of the singular value decomposition’, IEEE Trans. Image Process., 2001, 10, (5), pp. 724–735.
    23. 23)
      • 22. Pu, Y., Xu, Q., Wang, W.: ‘Image change detection based on cross-correlation coefficient by using genetic algorithm’. First Int. Conf. on Agro-Geoinformatics (Agro-Geoinformatics), 2012, 2012, pp. 1–5.
    24. 24)
      • 12. Chen, C., Zhang, S., Chen, Y.: ‘An image denoising method based on OMP and K-SVD’, Int. J. Adv. Comput. Technol., 2012, 4, (4), pp. 32–40.
    25. 25)
      • 9. Huang, N.E., Shen, Z., Long, S.R.: ‘The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis’. Proc. of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 1998, vol. 454, no. 1971, pp. 903–995.
    26. 26)
      • 18. Shao, R., Hu, W., Wang, Y.: ‘The fault feature extraction and classification of gear using principal component analysis and kernel principal component analysis based on the wavelet packet transform’, Measurement, 2014, 54, (6), pp. 118–132.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2016.0307
Loading

Related content

content/journals/10.1049/iet-spr.2016.0307
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading