Comparative analysis of variants of Gabor-Wigner Transform for crossterm reduction

• Autorzy: Ajab M. , Taj I. A. , Khan N. A.
• Języki publikacji: EN

Abstrakty

EN

Gabor Wigner Transform (GWT) is a composition of two time-frequency planes (Gabor Transform (GT) and Wigner Distribution (WD)), and hence GWT takes the advantages of both transforms (high resolution of WD and cross-terms free GT). In multi-component signal analysis where GWT fails to extract auto-components, the marriage of signal processing and image processing techniques proved their potential to extract autocomponents. The proposed algorithm maintained the resolution of auto-components. This work also shows that the Fractional Fourier Transform (FRFT) domain is a powerful tool for signal analysis. Performance analysis of modified fractional GWT reveals that it provides a solution of cross-terms of WD and blurring of GT.

Słowa kluczowe

EN

Wigner Distribution; Gabor transform; Gabor Wigner Transform; fractional Fourier transform

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2012
• Tom: Vol. 19, nr 3
• Strony: 499--508
• Opis fizyczny: Bibliogr. 33 poz., tab., wykr.

Twórcy

autor

Ajab M.

autor

Taj I. A.

autor

Khan N. A.

• Muhammad Ali Jinnah University (MAJU), Islamabad, Pakistan,

Bibliografia

• [1] Cohen, L. (1995). Time-Frequency Analysis. Prentice Hall, Englewood Cliffs, NJ.
• [2] Lusin, T., Agrez, D. (2011). Estimation of the amplitude square using the interpolated DFT. Metrol. Meas. Syst., 18(4), 583-596.
• [3] Hlawatch, F., Boudreaux-Bartels, G.F. (1992). Linear and quadratic time frequency signal representations. IEEE Signal Processing Magazine, 9(4), 21-67.
• [4] Shafi, I., Ahmad, J., Shah, S.I., Kashif, F.M. (2009). Techniques to Obtain Good Resolution and Concentrated Time-Frequency Distributions: A Review. EURASIP Journal on Advances in Signal processing. Artcle ID 673539, doi: 10.1155/2009/673539.
• [5] Boashash, B. (2003). Time-Frequency Signal Analysis and Processing. Prentice-Hall, Upper Saddle River, NJ, USA.
• [6] Cohen, L. (1989). Time-frequency distributions-A review. In Proc. IEEE, 77, 941-981.
• [7] Classen, T.A.C.M., Mecklenbrauker, W.F.G. (1980). The Wigner distribution - a tool for time-frequency signal analysis, part I: Continuous time signals. Philips J. Res., 35, 217-250.
• [8] Gröchenig, K. (2001). Foundations of Time-Frequency Analysis. Birkhäuser, Boston.
• [9] Lerga, J., Sucic, V., Boashash, B. (2011). An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR. EURASIP J. on Adv. In Signal processing, Artcle ID 725189, doi: 10.1155/2011/725189.
• [10] Hlawatsch, F., Flandrin, P. (1997). The interference structure of the Wigner distribution and related time-frequency signal representations, in The Wigner Distribution-Theory and Applications in Signal Processing, Elsevier, Amsterdam, Netherlands, 59-133.
• [11] Qian, S. (2002). Introduction to Time-Frequency and Wavelet Transforms. Upper Saddle River, New Jersey, Prentice-Hall.
• [12] Hlawatsch, F., Manickam, T.G., Urbanke, R.L., Jones, W. (1995). Smoothed pseudo-Wigner distribution, choi-williams distribution, and cone-kernel representation: Ambiguity-domain analysis and experimental comparison. Signal Process., 43(2).
• [13] Arce, G.R., Hasan, S.R. (2000). Elimination of interference terms of the discrete Wigner distribution using nonlinear filtering. IEEE Trans. Signal Processing, 48(8), 2321-2331.
• [14] Qazi, S., Georgakis, A., Stergioulas, L.K., Bahaei, M.S. (2007). Interference suppression in the Wigner distribution using fractional Fourier transformation and signal synthesis. IEEE Trans. Signal Process., 55, 3150-3154.
• [15] Khan, N.A., Taj, I.A., Jaffri, N., Ijaz, S. (2011). Cross-term elimination in Wigner distribution based on 2D signal processing techniques. Signal Processing, Advances in Fractional Signals and Systems, 91(3), 590-599.
• [16] Sejdic, E., Djurovic, I., Stankovic, L. (2011). Fractional Fourier transform as a signal processing tool: An overview of recent developments. Signal Processing, 91, 1351-1369.
• [17] Pei, S.C., Ding, J.J. (2007). Relations between Gabor transforms and fractional Fourier transforms and their applications for signal processing. IEEE Trans. Signal Processing, 55(10), 4839-4850.
• [18] Cho, S.H., Jang, G., Kwon, S.H. (2010). Time-Frequency Analysis of Power-Quality Disturbances via the Gabor-Wigner Transform. IEEE Trans. Power Deliver., 25(1), 494-499.
• [19] Szmajda, M., Górecki, K., Mroczka, J. (2010). Gabor Transform, SPWVD, Gabor-Wigner Transform and Wavelet Transform - Tools for Power Quality monitoring. Metrol. Meas. Syst., 17(3), 383-396.
• [20] Rioul, O., Vetterli, M. (1991). Wavelets and Signal Processing. IEEE SP Magazine, 8, 14-38.
• [21] Allen, R.L., Mills, D.W. (2004). Signal Analysis: Time, Frequency, Scale, and Structure. New York: Wiley-Interscience.
• [22] Hlawatsch, F. (1984). Interference terms in the Wigner distribution. In Proc. Int. Conf. on Digital Signal Processing, Florence, Italy, 363-367.
• [23] Stanković, L.J., Alieva, T., Bastiaans, M.J. (2003). Time-frequency signal analysis based on the windowed fractional Fourier transform. Signal Process., 83(11), 2459-2468.
• [24] Namias, V. (1980). The fractional order Fourier transform and its applications to quantum mechanics. J. Inst. Math Appl., 25, 241-265.
• [25] Mendlovic, D., Ozaktas, H.M. (1993). Fractional Fourier transforms and their optical implementation. J. Opt. Soc. Am. A, 10, 1875-1881.
• [26] Kutay, M.A., Ozaktas, H.M., Arikan, O., Onural, L. (1997). Optimal filter in fractional Fourier domains. IEEE Trans. Signal Process., 45(5), 1129-1143.
• [27] Almeida, L.B. (1994). The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process., 42, 3084-3091.
• [28] Saxena, R., Sing, K. (2005). Fractional Fourier transform: A novel tool for signal processing. J. Indian Institute of Science., 85, 11-26.
• [29] Acharya, T., Ray, A. (2005). Image Processing: Principles and Applications. Wiley Interscience, Hoboken, NJ.
• [30] Training a support vector machine in the primal, Neural Computation. (2007). 19(5), 1155-1178.
• [31] /http://www.dsp.rice.edu/software/TFA/RGK/BAT/batsig.bin.ZS.
• [32] Williams, W.J., Brown, M., Hero, A. (1991). Uncertainty, information and time frequency distributions. In SPIE, Advanced Signal Processing Algorithms, 1556, 144-156.
• [33] Jones, D., Park, T., (1992). A resolution comparison of several time-frequency representations. IEEE Trans. Signal Process., 40, 413-420.