EMD-based time-frequency analysis methods of audio signals

• Autorzy: Lewandowski Marcin , Deng Qizhang

Identyfikatory

DOI

10.24425/ijet.2024.149548

• Języki publikacji: EN

Abstrakty

EN

Using appropriate signal processing tools to analyze time series data accurately is essential for correctly interpreting the underlying processes. Commonly employed methods include kernel-based transforms that utilize base functions and modifications to depict time series data. This paper refers to the analysis of audio data using two such transforms: the Fourier transform and the wavelet transform, both based on assumptions regarding the signal's linearity and stationarity. However, in audio engineering, these assumptions often do not hold as the statistical characteristics of most audio signals vary over time, making them unsuitable for treatment as outputs from a Linear Time-Invariant (LTI) system. Consequently, more recent methods have shifted towards breaking down signals into various modes in an adaptive, data-specific manner, potentially offering benefits over traditional kernel-based methods. Techniques like empirical mode decomposition and Holo-Hilbert Spectral Analysis are examples of this. The effectiveness of these methods was tested through simulations using speech signals for both kernel-based and adaptive decomposition methods, demonstrating that these adaptive methods are effective for analyzing audio data that is both nonstationary and an output of the nonlinear system.

Słowa kluczowe

EN

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

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2024
• Tom: Vol. 70, No. 2
• Strony: 323--329
• Opis fizyczny: Bibliogr. 29 poz., wykr.

Twórcy

autor

Lewandowski Marcin

• Warsaw University of Technology

autor

Deng Qizhang

• University of New South Wales Sydney

Bibliografia

• [1] S. Bochner, "Fourier Integrals: Introduction to the Theory of Fourier Integrals. By EC Titchmarsh. Oxford, Clarendon Press, 1937.", Science, t. 87, nr2260, s. 370-370, 1938. https://www.science.org/doi/abs/10.1126/science.87.2260.370.a.
• [2] N. E. Huang et al., "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis", Proc. R. Soc. Lond. Ser. Math. Phys. Eng. Sci., t. 454, nr 1971, s. 903-995, mar. 1998, doi:10.1098/rspa.1998.0193. https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1998.0193.
• [3] P. J. Brockwell and 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., t. 25, nr 3, s. 235-238, 1977. https://ieeexplore.ieee.org/abstract/document/1162950
• [5] Y. Meyer, “Wavelets and Operators: Volume 1”. Cambridge university press, 1992. https://doi.org/10.1017/CBO9780511623820.
• [6] Z. Wu i N. E. Huang, "Ensemble empirical mode decomposition: a noise-assisted data analysis method", Adv. Adapt. Data Anal., t. 1, nr 01, s. 1-41, 2009. https://www.worldscientific.com/doi/abs/10.1142/S1793536909000047.
• [7] M. E. Torres, M. A. Colominas, G. Schlotthauer, and P. Flandrin, "A complete ensemble empirical mode decomposition with adaptive noise", in 2011 IEEE international conference on acoustics, speech and signal processing (ICASSP), 2011, s. 4144-4147. https://ieeexplore.ieee.org/abstract/document/5947265
• [8] M. A. Colominas, G. Schlotthauer, and M. E. Torres, "Improved complete ensemble EMD: A suitable tool for biomedical signal processing", Biomed. Signal Process. Control, t. 14, s. 19-29, 2014. https://www.sciencedirect.com/science/article/abs/pii/S1746809414000962
• [9] M. S. Fabus, A. J. Quinn, C. E. Warnaby, and M. W. Woolrich, "Automatic decomposition of electrophysiological data into distinct non-sinusoidal oscillatory modes", J. Neurophysiol., t. 126, nr 5, s. 1670-1684, 2021. https://journals.physiology.org/doi/full/10.1152/jn.00315.2021
• [10] R. Deering and J. F. Kaiser, "The use of a masking signal to improve empirical mode decomposition", in Proceedings.(ICASSP'05). IEEE Inter national Conference on Acoustics, Speech, and Signal Processing, 2005., 2005, t. 4, s. iv-485. https://ieeexplore.ieee.org/abstract/document/1416051
• [11] A. J. Quinn et al., "Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics", J. Neurophysiol., t. 126, nr 4, s. 1190-1208, 2021. https://journals.physiology.org/doi/full/10.1152/jn.00201.2021
• [12] Y. Yang, J. Deng, and D. Kang, "An improved empirical mode decomposition by using dyadic masking signals", Signal Image Video Process., t. 9, nr 6, s. 1259-1263, 2015. https://link.springer.com/article/10.1007/s11760-013-0566-7
• [13] O. B. Fosso and M. Molinas, "EMD mode mixing separation of signals with close spectral proximity in smart grids", w 2018 IEEE PES innovative smart grid technologies conference Europe (ISGT-Europe), 2018, s. 1-6. https://ieeexplore.ieee.org/abstract/document/8571816
• [14] S. Cole and B. Voytek, "Cycle-by-cycle analysis of neural oscillations", J. Neurophysiol., t. 122, nr 2, s. 849-861, 2019. https://journals.physiology.org/doi/full/10.1152/jn.00273.2019
• [15] A. V. Oppenheim, “Discrete-time signal processing”. Pearson Education India, 1999. https://dl.acm.org/doi/10.5555/294797
• [16] I. Daubechies, J. Lu, and H.-T. Wu, "Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool", Appl. Comput. Harmon. Anal., t. 30, nr 2, s. 243-261, 2011. https://www.sciencedirect.com/science/article/pii/S1063520310001016
• [17] F. Auger et al., "Time-frequency reassignment and synchrosqueezing: An overview", IEEE Signal Process. Mag., t. 30, nr 6, s. 32-41, 2013. https://ieeexplore.ieee.org/abstract/document/6633061
• [18] J. B. Elsner and A. A. Tsonis, “Singular spectrum analysis: a new tool in time series analysis”. Springer Science & Business Media, 1996. https://doi.org/10.1007/978-1-4757-2514-8.
• [19] M. G. Frei and I. Osorio, "Intrinsic time-scale decomposition: time-frequency-energy analysis and real-time filtering of nonstationary signals", Proc. R. Soc. Math. Phys. Eng. Sci., t. 463, nr 2078, s. 321-342, luty 2007, doi: 10.1098/rspa.2006.1761. https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2006.1761
• [20] P. Singh, S. D. Joshi, R. K. Patney, and K. Saha, "The Fourier decomposition method for nonlinear and nonstationary time series analysis", Proc. R. Soc. Math. Phys. Eng. Sci., t. 473, nr 2199, s. 20160871, 2017. https://royalsocietypublishing.org/doi/full/10.1098/rspa.2016.0871
• [21] N. E. Huang and in., "On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and nonstationary data", Philos. Trans. R. Soc. Math. Phys. Eng. Sci., t. 374, nr 2065, s. 20150206, kwi. 2016, doi: 10.1098/rsta.2015.0206. https://scholarlypublications.universiteitleiden.nl/handle/1887/112702
• [22] C.-H. Juan et al., "Revealing the dynamic nature of amplitude modulated neural entrainment with Holo-Hilbert spectral analysis", Front. Neurosci., t. 15, s. 673369, 2021. https://www.frontiersin.org/articles/10.3389/fnins.2021.673369/full
• [23] L. R. Rabiner, R. W. Schafer, and others, "Introduction to digital speech processing", Found. Trends® Signal Process., t. 1, nr 1-2, s. 1-194, 2007 https://doi.org/10.1561/2000000001.
• [24] J. Benesty, M. M. Sondhi, Y. Huang, and others, Springer handbook of speech processing, t. 1. Springer, 2008. https://link.springer.com/book/10.1007/978-3-540-49127-9
• [25] D. Kapilow, Y. Stylianou, and J. Schroeter, "Detection of non-stationarity in speech signals and its application to time-scaling", 1999. https://doi.org/10.21437/Eurospeech.1999-503.
• [26] R. S. Holambe and M. S. Deshpande, Advances in nonlinear modeling for speech processing. Springer Science & Business Media, 2012. https://link.springer.com/book/10.1007/978-1-4614-1505-3
• [27] 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., t. 11, nr 13, s. 3868, 2022. https://www.mdpi.com/2077-0383/11/13/3868
• [28] N. Moradi, P. LeVan, B. Akin, B. G. Goodyear, and R. C. Sotero, "Holo-Hilbert spectral-based noise removal method for EEG high-frequency bands", J. Neurosci. Methods, t. 368, s. 109470, 2022. https://www.sciencedirect.com/science/article/abs/pii/S0165027021004052
• [29] W.-K. Liang, P. Tseng, J.-R. Yeh, N. E. Huang, and C.-H. Juan, "Frontoparietal beta amplitude modulation and its interareal cross-frequency coupling in visual working memory", Neuroscience, t. 460, s. 69-87, 2021. https://www.sciencedirect.com/science/article/abs/pii/S0306452221000865