EMD-based time-frequency analysis methods of non-stationary audio signals

• Autorzy: Lewandowski Marcin , Grodzicka Salomea

Identyfikatory

DOI

10.21008/j.0860-6897.2022.2.15

• Języki publikacji: EN

Abstrakty

EN

To ensure that any time series data is appropriately interpreted, it should be analyzed with proper signal processing tools. The most common analysis methods are kernel-based transforms, which use base functions and their modifications to represent time series data. This work discusses an analysis of audio data and two of those transforms - the Fourier transform and the wavelet transform based on a priori assumptions about the signal's linearity and stationarity. In audio engineering, these assumptions are invalid because the statistical parameters of most audio signals change with time and cannot be treated as an output of the LTI system. That is why recent approaches involve decomposition of a signal into different modes in a data-dependent and adaptive way, which may provide advantages over kernel-based transforms. Examples of such methods include empirical mode decomposition (EMD), ensemble EMD (EEMD), variational mode decomposition (VMD), or singular spectrum analysis (SSA). Simulations were performed with speech signal for kernel-based and data-dependent decomposition methods, which revealed that evaluated decomposition methods are promising approaches to analyzing non-stationary audio data.

Słowa kluczowe

EN

empirical mode decomposition; non-stationary audio data; time-frequency analysis

PL

empiryczna metoda dekompozycji; niestacjonarne dane dźwiękowe; analiza czasowo-częstotliwościowa

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2022
• Tom: Vol. 33, nr 2
• Strony: art. no. 2022215
• Opis fizyczny: Bibliogr. 32 poz., wykr.

Twórcy

autor

Lewandowski Marcin

• Warsaw University of Technology, Institute of Radioelectronics and Multimedia Technology, Faculty of Electronics and Information Technology, Nowowiejska 15/19, 00-665 Warsaw

• https://orcid.org/0000-0002-8106-1213

autor

Grodzicka Salomea

• Warsaw University of Technology, Institute of Radioelectronics and Multimedia Technology, Faculty of Electronics and Information Technology, Nowowiejska 15/19, 00-665 Warsaw

• https://orcid.org/0000-0002-7286-6933

Bibliografia

• 1. S. Bochner; Fourier Integrals: Introduction to the Theory of Fourier Integrals. By EC Titchmarsh. Oxford, Clarendon Press, 1937; Science, 87, 2260, 370, 1938.
• 2. N.E. Huang et al.; The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. Ser. Math. Phys. Eng. Sci., 1998, 454(1971), 903-995. DOI:10.1098/rspa.1998.0193.
• 3. P.J. Brockwell, R. A. Davis; Time series: theory and methods. Springer science & business media, 2009.
• 4. J. Allen; Short term spectral analysis, synthesis, and modification by discrete Fourier transform; IEEE Trans. Acoust. Speech Signal Process., 1977, 25(3), 235-238.
• 5. Y. Meyer; Wavelets and Operators: Volume 1; Cambridge University Press, 1992.
• 6. Z. Wu, N. E. Huang; Ensemble empirical mode decomposition: a noise-assisted data analysis method; Adv. Adapt. Data Anal., 2009, 1(1), 1-41.
• 7. M.E. Torres, M.A. Colominas, G. Schlotthauer, P. Flandrin; A complete ensemble empirical mode decomposition with adaptive noise; In: IEEE international conference on acoustics, speech and signal processing (ICASSP), 2011, 4144-4147.
• 8. M.A. Colominas, G. Schlotthauer, M.E. Torres; Improved complete ensemble EMD: A suitable tool for biomedical signal processing; Biomed. Signal Process. Control, 2014, 14, 19-29.
• 9. T. Liu, Z. Luo, J. Huang, S. Yan; A comparative study of four kinds of adaptive decomposition algorithms and their applications; Sensors, 2018, 8(7), 2120.
• 10. K. Dragomiretskiy, D. Zosso; Variational mode decomposition; IEEE Trans. Signal Process., 2013, 62(3), 531-544.
• 11. V.R. Carvalho, M.F. Moraes, A.P. Braga, E.M. Mendes; Evaluating five different adaptive decomposition methods for EEG signal seizure detection and classification; Biomed. Signal Process. Control, 2020, 62, 102073.
• 12. M.S. Fabus, A.J. Quinn, C.E. Warnaby, M.W. Woolrich; Automatic decomposition of electrophysiological data into distinct nonsinusoidal oscillatory modes; J. Neurophysiol., 2021, 126(5), 1670-1684.
• 13. R. Deering, J.F. Kaiser; The use of a masking signal to improve empirical mode decomposition; In: Proceedings ICASSP'05, IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., 4, iv-485.
• 14. A.J. Quinn, et al.; Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics; J. Neurophysiol., 2021, 126(4), 1190-1208.
• 15. Y. Yang, J. Deng, D. Kang; An improved empirical mode decomposition by using dyadic masking signals; Signal Image Video Process., 2015, 9(6), 1259-1263.
• 16. O.B. Fosso, M. Molinas; EMD mode mixing separation of signals with close spectral proximity in smart grids; 2018 IEEE PES innovative smart grid technologies conference Europe (ISGT-Europe), 2018, 1-6.
• 17. S. Cole; B. Voytek; Cycle-by-cycle analysis of neural oscillations; J. Neurophysiol., 2019, 122(2), 849-861.
• 18. A.V. Oppenheim; Discrete-time signal processing; Pearson Education India, 1999.
• 19. Daubechies, J. Lu, H.-T. Wu; Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool; Appl. Comput. Harmon. Anal., 2011, 30(2), 243-261.
• 20. F. Auger, et al.; Time-frequency reassignment and synchrosqueezing: An overview; IEEE Signal Process. Mag., 2013, 30(6), 32-41.
• 21. J.B. Elsner, A.A. Tsonis; Singular spectrum analysis: a new tool in time series analysis; Springer Science & Business Media, 1996.
• 22. M. G. Frei, I. Osorio; Intrinsic time-scale decomposition: time-frequency-energy analysis and real-time filtering of non-stationary signals; Proc. R. Soc. Math. Phys. Eng. Sci., 2007, 463(2078), 321-342. DOI:10.1098/rspa.2006.1761.
• 23. P. Singh, S.D. Joshi, R.K. Patney, K. Saha; The Fourier decomposition method for nonlinear and non-stationary time series analysis; Proc. R. Soc. Math. Phys. Eng. Sci., 2017, 473, 2199, 20160871.
• 24. L.R. Rabiner, R. W. Schafer, et al.; Introduction to digital speech processing; Found. Trends® Signal Process., 2007, 1(1-2), 1-194.
• 25. J. Benesty, M.M. Sondhi, Y. Huang, et al.; Springer handbook of speech processing, vol.1. Springer, 2008.
• 26. D. Kapilow, Y. Stylianou, J. Schroeter; Detection of non-stationarity in speech signals and its application to time-scaling; Sixth European Conference on Speech Communication and Technology, EUROSPEECH 1999, Budapest, Hungary, September 5-9, 1999. DOI:10.21437/Eurospeech.1999-503
• 27. R.S. Holambe, M.S. Deshpande, Advances in non-linear modeling for speech processing. Springer Science & Business Media, 2012.
• 28. N.E. Huang et al.; On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data; Philos. Trans. R. Soc. Math. Phys. Eng. Sci., 2016, 374, 2065, 20150206. DOI:10.1098/rsta.2015.0206.
• 29. P.-L. Lee et al.; The Full Informational Spectral Analysis for Auditory Steady-State Responses in Human Brain Using the Combination of Canonical Correlation Analysis and Holo-Hilbert Spectral Analysis; J. Clin. Med., 2022, 11(13), 3868.
• 30. N. Moradi, P. LeVan, B. Akin, B.G. Goodyear, R.C. Sotero; Holo-Hilbert spectral-based noise removal method for EEG high-frequency bands; J. Neurosci. Methods, 2022, 368, 109470.
• 31. W.-K. Liang, P. Tseng, J.-R. Yeh, N.E. Huang, C.-H. Juan; Frontoparietal beta amplitude modulation and its interareal cross-frequency coupling in visual working memory; Neuroscience, 2021, 460, 69-87.
• 32. C.-H. Juan et al.; Revealing the dynamic nature of amplitude modulated neural entrainment with Holo-Hilbert spectral analysis; Front. Neurosci., 2021, 15, 673369.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).