Abstract
This chapter deals with the various techniques associated with the analysis of self similar structures of music signals as well as bio-signals obtained from EEG data. This chapter is basically a detailed analysis on the following tools of complex data analysis which have been elaborated later in the different studies.
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1.
Wavelet analysis
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2.
Detrended fluctuation analysis (DFA)
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3.
Multifractal detrended fluctuation analysis (MFDFA)
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4.
Multifractal cross correlation analysis (MFDXA)
All these techniques make use of Fractal Dimension (FD) or multifractal spectral width (obtained as an output of the MFDFA technique) as an important parameter with which the emotional arousal corresponding to a certain cognitive task (in this case a particular music clip) can be quantified. MFDXA can prove to be an important tool with which the degree of cross correlation between two non-linear EEG signals originating from different lobes of brain can be accurately measured during higher order cognitive tasks. With this, we can have a quantitative assessment of how the different lobes are cross-correlated during higher order thinking tasks or during the perception of audio or any other stimuli. MFDXA can also prove to be an amazing tool in music signal analysis, where we can estimate the degree of cross-correlation between two non-linear self-similar musical clips. A higher degree of cross-correlation would imply that both the signals are very much similar in certain aspects. This in turn can be used as an important tool to obtain a cue for improvisation in musical performances as well as in the identification of presence of Ragas in songs. Several other tools for EEG feature extraction have also been discussed in detail here which include novel methods like neural jitter-shimmer as well as extraction of pitch of EEG signals.
Clouds are not spheres, mountains are not cones,
coastlines are not circles,
and bark is not smooth,
nor does lightning travel in a straight line
—Benoit Mandelbrot
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References
Akin, M., Arserim, M. A., Kiymik, M. K., & Turkoglu, I. (2001). A new approach for diagnosing epilepsy by using wavelet transform and neural networks. In Engineering in Medicine and Biology Society, 2001. Proceedings of the 23rd Annual International Conference of the IEEE (Vol. 2, pp. 1596–1599). IEEE.
Ashkenazy, Y., Baker, D. R., Gildor, H., & Havlin, S. (2003). Nonlinearity and multifractality of climate change in the past 420,000Â years. Geophysical research letters, 30(22).
Banerjee, A., Sanyal, S., Patranabis, A., Banerjee, K., Guhathakurta, T., & Sengupta, R. (2016). Study on brain dynamics by non linear analysis of music induced EEG signals. Physica A: Statistical Mechanics and its Applications, 444, 110–120.
Berument, H., Ceylan, N. B., & Dogan, N. (2010). The impact of oil price shocks on the economic growth of selected MENA countries. Energy Journal, 31(1), 149.
Bizopoulos, P. A., Al-Ani, T., Tsalikakis, D. G., Tzallas, A. T., Koutsouris, D. D., & Fotiadis, D. I. (2013, July). An automatic electroencephalography blinking artefact detection and removal method based on template matching and ensemble empirical mode decomposition. In Engineering in Medicine and Biology Society (EMBC), 2013 35th Annual International Conference of the IEEE (pp. 5853–5856). IEEE.
Bracewell, R. N. (1965). The fourier transform and is applications. New York, 5.
Buzsáki, G., Anastassiou, C. A., & Koch, C. (2012). The origin of extracellular fields and currents—EEG, ECoG, LFP and spikes. Nature reviews neuroscience, 13(6), 407–420.
Chen, S. S. (2009). Oil price pass-through into inflation. Energy Economics, 31(1), 126–133.
Dimoulas, C., Kalliris, G., Papanikolaou, G., & Kalampakas, A. (2007). Long-term signal detection, segmentation and summarization using wavelets and fractal dimension: A bioacoustics application in gastrointestinal-motility monitoring. Computers in Biology and Medicine, 37(4), 438–462.
Farrús, M., & Hernando, J. (2009). Using jitter and shimmer in speaker verification. IET Signal Processing, 3(4), 247–257.
Feder, J. (2013). Fractals. Springer Science & Business Media.
Figliola, A., Serrano, E., Rostas, J. A. P., Hunter, M., & Rosso, O. A. (2007, May). Study of EEG brain maturation signals with multifractal detrended fluctuation analysis. In AIP Conference Proceedings (Vol. 913, No. 1, pp. 190–195). AIP.
Gao, T. T., Wu, D., Huang, Y. L., & Yao, D. Z. (2007). Detrended fluctuation analysis of the human EEG during listening to emotional music. Journal of Electronic Science and Technology, 5(3), 272–277.
Ghosh, D., Dutta, S., & Chakraborty, S. (2014). Multifractal detrended cross-correlation analysis for epileptic patient in seizure and seizure free status. Chaos, Solitons & Fractals, 67, 1–10.
Hardstone, R., Poil, S. S., Schiavone, G., Jansen, R., Nikulin, V. V., Mansvelder, H. D., & Linkenkaer-Hansen, K. (2012). Detrended fluctuation analysis: a scale-free view on neuronal oscillations. Frontiers in physiology, 3.
Hazarika, N., Chen, J. Z., Tsoi, A. C., & Sergejew, A. (1997). Classification of EEG signals using the wavelet transform. Signal Processing, 59(1), 61–72.
He, L. Y., & Chen, S. P. (2011). Multifractal detrended cross-correlation analysis of agricultural futures markets. Chaos, Solitons & Fractals, 44(6), 355–361.
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., … & Liu, H. H. (1998, March). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences (Vol. 454, No. 1971, pp. 903–995). The Royal Society.
Jiang, Z. Q., & Zhou, W. X. (2011). Multifractal detrending moving-average cross-correlation analysis. Physical Review E, 84(1), 016106.
Johnston, D. (1999). Cool edit 2000. Computer software. Phoenix, AZ: Syntrillium Software.
Jones, C. M., & Kaul, G. (1996). Oil and the stock markets. The Journal of Finance, 51(2), 463–491.
Jung, C. Y., & Saikiran, S. S. (2016). A review on EEG artifacts and its different removal technique.
Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., & Stanley, H. E. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and its Applications, 316(1), 87–114.
Karkare, S., Saha, G., & Bhattacharya, J. (2009). Investigating long-range correlation properties in EEG during complex cognitive tasks. Chaos, Solitons & Fractals, 42(4), 2067–2073.
Kedem, B. (1986). Spectral analysis and discrimination by zero-crossings. Proceedings of the IEEE, 74(11), 1477–1493.
Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J. (2001). Long-range temporal correlations and scaling behavior in human brain oscillations. Journal of Neuroscience, 21(4), 1370–1377.
Maity, A. K., Pratihar, R., Mitra, A., Dey, S., Agrawal, V., Sanyal, S., et al. (2015). Multifractal detrended fluctuation analysis of alpha and theta EEG rhythms with musical stimuli. Chaos, Solitons & Fractals, 81, 52–67.
Mehrotra, K., Mohan, C. K., & Ranka, S. (1997). Elements of artificial neural networks. Cambridge: MIT press.
Movahed, M. S., & Hermanis, E. (2008). Fractal analysis of river flow fluctuations. Physica A: Statistical Mechanics and its Applications, 387(4), 915–932.
Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., & Goldberger, A. L. (1994). Mosaic organization of DNA nucleotides. Physical Review E, 49(2), 1685.
Podobnik, B., & Stanley, H. E. (2008). Detrended cross-correlation analysis: A new method for analyzing two nonstationary time series. Physical Review Letters, 100(8), 084102.
Podobnik, B., Grosse, I., Horvatić, D., Ilic, S., Ivanov, P. C., & Stanley, H. E. (2009). Quantifying cross-correlations using local and global detrending approaches. The European Physical Journal B, 71(2), 243–250.
Podobnik, B., Horvatic, D., Ng, A. L., Stanley, H. E., & Ivanov, P. C. (2008). Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes. Physica A: Statistical Mechanics and its Applications, 387(15), 3954–3959.
Podobnik, B., Jiang, Z. Q., Zhou, W. X., & Stanley, H. E. (2011). Statistical tests for power-law cross-correlated processes. Physical Review E, 84(6), 066118.
Reboredo, J. C., Rivera-Castro, M. A., & Zebende, G. F. (2014). Oil and US dollar exchange rate dependence: A detrended cross-correlation approach. Energy Economics, 42, 132–139.
Roads, C. (1996). The computer music tutorial. Cambridge: MIT press.
Scheirer, E., & Slaney, M. (1997, April). Construction and evaluation of a robust multifeature speech/music discriminator. In Acoustics, Speech, and Signal Processing, 1997. ICASSP-97, 1997 IEEE International Conference on (Vol. 2, pp. 1331–1334). IEEE.
Selesnick, I. W., Baraniuk, R. G., & Kingsbury, N. C. (2005). The dual-tree complex wavelet transform. IEEE Signal Processing Magazine, 22(6), 123–151.
Sivanandam, S. N., & Deepa, S. N. (2006). Introduction to neural networks using Matlab 6.0. New York: Tata McGraw-Hill Education.
Sjölander, K., & Beskow, J. (2000). Wavesurfer-an open source speech tool. In Sixth International Conference on Spoken Language Processing.
Wang, F., Liao, G. P., Zhou, X. Y., & Shi, W. (2013). Multifractal detrended cross-correlation analysis for power markets. Nonlinear Dynamics, 72(1–2), 353–363.
Xu, N., Shang, P., & Kamae, S. (2010). Modeling traffic flow correlation using DFA and DCCA. Nonlinear Dynamics, 61(1–2), 207–216.
Zhou, W. X. (2008). Multifractal detrended cross-correlation analysis for two nonstationary signals. Physical Review E, 77(6), 066211.
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Ghosh, D., Sengupta, R., Sanyal, S., Banerjee, A. (2018). Non Linear Techniques for Studying Complex Systems. In: Musicality of Human Brain through Fractal Analytics. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-6511-8_2
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