Time Frequency analysis of Non-Stationary signals by Differential frequency window S –Transform

  • Authors

    • B Murali Krishna
    • M Srinivas
    • S Raja Gopal
    • G L. P. Ashok
    2018-03-18
    https://doi.org/10.14419/ijet.v7i2.7.11086
  • Newton Raphson method, S-Transform, Localization, ECG.
  • The S transform is an extension of Short Time Fourier Transform and Wavelet transform, has a time frequency resolution which is far from ideal. A differential frequency window is proposed in this paper to enhance the time frequency energy localization. When a non stationary signal consists of abrupt amplitude variation equal to peak of Gaussian function at initial intervals of chosen guassian window, then some part of the signal amplitude will be nullified during transform projection. The major function of differential frequency window is to track all abrupt amplitude-frequency variations which exploits in non – stationary signals. A mathematical method namely Newton Raphson method is adopted for this trace. The proposed scheme is tested for ECG data in presence of noise environment and results shows that proposed algorithm produces better enhanced energy localization in comparison to the standard S – Transform, STFT, and CWT. Furthermore the above algorithm is implemented on FPGA for real time applications.

     

     

  • References

    1. [1] CRAMÉR H., “On some classes of non stationary stochastic processesâ€, Proc. 4th Berkeley Sympos. Math. Stat. Prob., University of California Press, pp. 57–78, 1961.

      [2] B. Boashash, Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier, Amsterdam; Boston, 2003.

      [3] Cohen L. Time–frequency analysis. Englewood Cliffs, NJ: Prentice-Hall, PTR; 1995.

      [4] Tolimieri, Richard, and Myoung An, eds. Time-frequency representations. Springer, 1998.

      [5] Stockwell, Robert Glenn. "A basis for efficient representation of the S-transform." Digital Signal Processing 17.1 (2007): 371-393.

      [6] Goswami, Jaideva C., and Andrew K. Chan. Fundamentals of wavelets: theory, algorithms, and applications. Vol. 233. John Wiley & Sons, 2011.

      [7] Mallat, Stéphane. A wavelet tour of signal processing. Academic press, 1999.

      [8] Stockwell, Robert Glenn, Lalu Mansinha, and R. P. Lowe. "Localization of the complex spectrum: the S transform." Signal Processing, IEEE Transactions on44.4 (1996): 998-1001.

      [9] STOCKWELL R.G., Why use the S transform?, in Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis, Editors: L. Rodino, B.-W. Schulze and M.W.Wong, Fields Institute Communications Series 52, American Mathematical Society, 2007, 279–309.

      [10] Boashash B. Estimating and interpreting the instantaneous frequency of a signal—part 1: fundamentals. Proc IEEE 1992; 80(4):520–38.

      [11] Dash, P. K., K. B. Panigrahi, and G. Panda. "Power quality analysis using S-transform." Power Delivery, IEEE Transactions on 18.2 (2003): 406-411.

      [12] Assous and Boashash: Evaluation of the modified S transform for time-frequency synchrony analysis and source localisation. EURASIP Journal on Advances in Signal Processing 2012 2012:49.

      [13] Djurović, Igor, Ervin Sejdić, and Jin Jiang. "Frequency-based window width optimization for S-transform." AEU-International Journal of Electronics and Communications 62.4 (2008): 245-250.

      [14] WONG M.W., Wavelet Transforms and Localization Operators, Operator Theory: Advances and Applications 136, Birkh¨auser, 2002.

      [15] Case, William B. "Wigner functions and Weyl transforms for pedestrians."American Journal of Physics 76.10 (2008): 937-946.

      [16] Bedrosian, E. (December 1962), "A Product Theorem for Hilbert Transforms", Rand Corporation Memorandum (RM-3439-PR)

      [17] B. Boashash, P. O'Shea, Polynomial Wigner–Ville distributions and their relationship to time varying higher order spectra, IEEE Transactions on Signal Processing 42(1994)216–220.

      [18] Ypma, Tjalling J. "Historical development of the Newton-Raphson method."SIAM review 37.4 (1995): 531-551.

      [19] Deekshitulu, G. V. S. R., and J. Jagan Mohan. "Fractional difference inequalities." Communications in Applied Analysis 14.1 (2010): 89.

      [20] Georgilakis, P. S. "Recursive genetic algorithm-finite element method technique for the solution of transformer manufacturing cost minimisation problem." iet electric power applications 3.6 (2009): 514-519.

      [21] Davis, Lawrence, ed. Handbook of genetic algorithms. Vol. 115. New York: Van Nostrand Reinhold, 1991.

      [22] Moukadem, Ali, et al. "Stockwell transform optimization applied on the detection of split in heart sounds." Signal Processing Conference (EUSIPCO), 2013 Proceedings of the 22nd European. IEEE, 2014.

      [23] Ramachandran, Seetharaman. Digital VLSI Systems Design: A Design Manual for Implementation of Projects on FPGAs and ASICs Using Verilog. Springer Science & Business Media, 2007.

      [24] Meyer-Bäse, Uwe, Anke Meyer-Bäse, and Wolfgang Hilberg. "Coordinate rotation digital computer (CORDIC) synthesis for FPGA." Field-Programmable Logic Architectures, Synthesis and Applications. Springer Berlin Heidelberg, 1994. 397-408.

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  • How to Cite

    Murali Krishna, B., Srinivas, M., Raja Gopal, S., & L. P. Ashok, G. (2018). Time Frequency analysis of Non-Stationary signals by Differential frequency window S –Transform. International Journal of Engineering & Technology, 7(2.7), 878-882. https://doi.org/10.14419/ijet.v7i2.7.11086