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Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement Cover

Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement

Measurement Science Review
Volume 15 (2015): Issue 3 (June 2015)
By: ,  ,  ,   and    
Open Access
|Jul 2015
References

References

  1. [1] Sabatier, J., Agrawal, O.P., Machado, J.T. (2007).. Springer.
    Open DOISearch in Google Scholar
  2. [2] Toman, J.J., Brown, S.D. (1981). Peak resolution by semi-derivative voltammetry., 53 (9), 1497-1504.
    Open DOISearch in Google Scholar
  3. [3] Bobrowski, A., Kasprzyk, G., Mocák, J. (2000). Theoretical and experimental resolution of semiderivative linear scan voltammetry., 65 (6), 979-994.
    Open DOISearch in Google Scholar
  4. [4] Kharintsev, S.S., Salakhov, M.K. (2004). A simple method to extract spectral parameters using fractional derivative spectrometry., 60 (8), 2125-2133.
    Open DOISearch in Google Scholar
  5. [5] Mocak, J., Janiga, I., Rievaj, M., Bustin, D. (2007). The use of fractional differentiation or integration for signal improvement., 7 (5), 39-42.
    Search in Google Scholar
  6. [6] Xiaoquan, L., Hongde, L., Min, Z., Xiaoqiang, W., Zhonghua, X., Jingwan, K. (2003). Fractional derivative combined fourier-least square fitting to process noised overlapped signal., 31 (2), 143-147.
    Search in Google Scholar
  7. [7] Li, Y.L., Tang, H.Q., Chen, H.X. (2011). Fractional-order derivative spectroscopy for resolving simulated overlapped Lorenztian peaks., 107 (1), 83-89.
    Open DOISearch in Google Scholar
  8. [8] Pu, Y., Wang, W., Zhou, J., Wang, Y., Jia, H. (2008). Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation., 51 (9), 1319-1339.
    Open DOISearch in Google Scholar
  9. [9] Mathieu, B., Melchior, P., Oustaloup, A., Ceyral, C. (2003). Fractional differentiation for edge detection., 83 (11), 2421-2432.
    Open DOISearch in Google Scholar
  10. [10] Gao, C., Zhou, J., Zheng, X., Lang, F. (2011). Image enhancement based on improved fractional differentiation., 7 (1), 257-264.
    Search in Google Scholar
  11. [11] Gao, C.B., Zhou, J.L., Hu, J.R., Lang, F.N. (2011). Edge detection of colour image based on quaternion fractional differential., 5 (3), 261-272.
    Open DOISearch in Google Scholar
  12. [12] Cuesta, E., Kirane, M., Malik, S.A. (2012). Image structure preserving denoising using generalized fractional time integrals., 92 (2), 553-563.
    Open DOISearch in Google Scholar
  13. [13] Ren, Z., He, C., Zhang, Q. (2013). Fractional order total variation regularization for image super-resolution., 93 (9), 2408-2421.
    Open DOISearch in Google Scholar
  14. [14] Khanna, S., Chandrasekaran, V. (2012). Fractional derivative filter for image contrast enhancement with order prediction. In. IEEE, 1-6.
    Open DOISearch in Google Scholar
  15. [15] Krishna, B.T. (2011). Studies on fractional order differentiators and integrators: A survey., 91 (3), 386-426.
    Open DOISearch in Google Scholar
  16. [16] Podlubny, I. (1998).(Vol. 198). Academic Press.
    Search in Google Scholar
  17. [17] Chen, D., Chen, Y.Q., Xue, D. (2011). Digital fractional order Savitzky-Golay differentiator., 58 (11), 758-762.
    Open DOISearch in Google Scholar
  18. [18] Tseng, C.C., Lee, S.L. (2010). Design of fractional order digital differentiator using radial basis function., 57 (7), 1708-1718.
    Open DOISearch in Google Scholar
  19. [19] Tseng, C.C. (2001). Design of fractional order digital FIR differentiators., 8 (3), 77-79.
    Open DOISearch in Google Scholar
  20. [20] Tseng, C.C. (2007). Design of FIR and IIR fractional order Simpson digital integrators., 87 (5), 1045-1057.
    Open DOISearch in Google Scholar
  21. [21] Tseng, C.C., Pei, S.C., Hsia, S.C. (2000). Computation of fractional derivatives using Fourier transform and digital FIR differentiator., 80 (1), 151-159.
    Open DOISearch in Google Scholar
  22. [22] Tseng, C.C. (2006). Design of variable and adaptive fractional order FIR differentiators., 86 (10), 2554-2566.
    Open DOISearch in Google Scholar
  23. [23] Chen, Y., Vinagre, B.M. (2003). A new IIR-type digital fractional order differentiator., 83 (11), 2359-2365.
    Open DOISearch in Google Scholar
  24. [24] Li, Y., Sun, N. (2011). Numerical solution of fractional differential equations using the generalized block pulse operational matrix., 62 (3), 1046-1054.
    Open DOISearch in Google Scholar
  25. [25] Ferdi, Y. (2009). Impulse invariance-based method for the computation of fractional integral of order 0< α< 1., 35 (5), 722-729.
    Open DOISearch in Google Scholar
  26. [26] Griffiths, T.R., King, K., Hubbard, H.V.S.A., Schwing-Weill, M.J., Meullemeestre, J. (1982). Some aspects of the scope and limitations of derivative spectroscopy., 143, 163-176.
    Open DOISearch in Google Scholar
  27. [27] O'Haver, T.C., Fell, A.F., Smith, G. et al. (1982). Derivative spectroscopy and its applications in analysis. In, 19 (1), 22-46.
    Open DOISearch in Google Scholar
  28. [28] Shao, X., Cai, W., Sun, P., Zhang, M., Zhao, G. (1997). Quantitative determination of the components in overlapping chromatographic peaks using wavelet transform., 69 (9), 1722-1725.
    Open DOISearch in Google Scholar
  29. [29] Chi-Hsu, W. (1983). On the generalization of block pulse operational matrices for fractional and operational calculus., 315 (2), 91-102.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.1515/msr-2015-0015 | Journal eISSN: 1335-8871
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Language: English
Page range: 101 - 106
Submitted on: Nov 18, 2014
Accepted on: Jun 18, 2015
Published on: Jul 10, 2015
Published by: Slovak Academy of Sciences, Institute of Measurement Science
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
Keywords:
Haar wavelet,
non–integer order calculus,
operational matrix,
signal enhancement
Related subjects:
Engineering,
Electrical engineering,
Control engineering, metrology and testing

© 2015 Yuanlu Li, Chang Pan, Xiao Meng, Yaqing Ding, Haixiu Chen, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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