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Speech, Music and Multifractality
Audio signal categorization is one of the rudimentary steps in applications like content-based audio information retrieval, audio indexing, speaker identification, and so on. In this work, a rigorous, non-stationary methodology capable of categorization among speech and various music signals is proposed. Multifractal detrended fluctuation analysis method is used to analyse the internal dynamics of the acoustics of digitized audio signal. The test data include speech (nonmusical), drone (periodically musical) and music samples of Rāgas (having different musicality) from Indian classical music (INDIC). It is found that the degree of complexity and multifractality (measured by width of the multifractal spectrum) changes from the start towards the end of each audio sample. However, the range of this variation is the smallest for speech and drone. The normalized value of the width of the multifractal spectrum is strikingly different for speech and drone. Experimental results show that this parameter can effectively classify speech and drone signals. Further, we have experimented with a number of clips of INDIC Rāgas with a range of variation in musicality and mood content. The results show that the width of the multifractal spectrum of the signals can categorize different music signals. In contrast with the conventional stationary techniques for audio signal analysis, we have used the method of complexity analysis without converting the non-stationary audio signals in frequency domain. We have used basic waveforms of the audio signals after de-noising them.
Keywords
Classical Music, Drone, Multifractal Analysis, Speech.
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- Hsu, K. J. and Hsu, A. J., Fractal geometry of music. Proc. Natl. Acad. Sci. USA, 1990, 87(3), 938–941.
- Mandelbrot, B.. The Fractal Geometry of Nature, Henry Holt and Company, 1983, vol. 51(3), pp. 384–391.
- Chen, Z., Ivanov, P. Ch., Hu, K. and Stanley, H. E., Effect of nonstationarities on detrended fluctuation analysis. Phys. Rev. E., 2002, 65(4), 041107–041111.
- Haar, J. and Palisca, C. V., Humanism in Italian Renaissance Musical Thought, Renaiss, Q., 1988, vol. 41(1), pp. 138–156.
- Madden, C. B., Fractals in Music: Introductory Mathematics for Musical Analysis, High Art Press, Salt Lake City, 1999.
- Voss, R. F., 1/f noise in music: Music from 1/f noise. J. Acoust. Soc. Am., 1978, 63(1), 258–263.
- Bak, P., Tang, C. and Wiesenfeld, K., Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett., 1987, 59(4), 381–384.
- Tricot, C., Dimension fractale et spectre. J. Chim. Phys., 1988, 85(1), 379–382.
- Hsü, K. J. and Hsü, A., Self-similarity of the 1/f noise called music. Proc. Natl. Acad. Sci. USA, 1991, 88(8), 3507–3509.
- Hausdorff, J. M., Purdon, P. L., Peng, C. K., Ladin, Z., Wei, J. W. and Goldberger, A. L., Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. J. Appl. Physiol., 1996, 80(5), 1448–1457.
- Shi, Y., Correlations of pitches in music. Fractals, 1996, 4(4), 547–553.
- Gunduz, G. and Gunduz, U., The mathematical analysis of the structure of some songs. Physica A Stat. Mech., 2005, 357(3–4), 565–592.
- Buldyrev, S. V., Goldberger, A. L., Havlin, S., Peng, C. K., Stanley, H. E. and Stanley, M. H. R., Fractal landscapes and molecular evolution: analysis of myosin heavy chain genes. Biophys. J., 1993, 65(6), 2673–2679.
- Kantelhardt, J. W., Koscielny-Bunde, E., Rego, H. H. A., Havlin, S. and Bunde, A., Detecting long-range correlations with detrended fluctuation analysis. Physica A Stat. Mech., 2001, 295(3–4), 441–454.
- Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Bunde, A., Havlin, S. and Stanley, H. E., Multifractal detrended fluctuation analysis of nonstationary time series. Physica A Stat. Mech., 2002, 316(1–4), 87–114.
- Serranoa, E. and Figliola, A., Wavelet Leaders: a new method to estimate the multifractal singularity spectra. Physica A Stat. Mech., 2009, 388(14), 2793–2805.
- Oswiecimka, P., Kwapien, J. and Drozdz, S., Wavelet versus detrended fluctuation analysis of multifractal structures. Phys. Rev. E, 2006, 74(1), 016103–016109.
- Huang, Y. X., Schmitt, F. G., Hermand, J. P. and Gagne, Y., Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: a comparison study with detrended fluctuation analysis and wavelet leaders. Phys. Rev. E, 2011, 84(1), 016208– 016215.
- Su, Z. Y. and Wu, T., Multifractal analyses of music sequences. Physica D: Nonlinear Phenom., 2006, 221(2), 188–194.
- Jafari, G. R., Pedram, P. and Hedayatifar, L., Long-range correlation and multifractality in bach’s inventions pitches. J. Stat. Mech. Theory Exp., 2007, 4, 04012–04019.
- Chakraborty, S., Krishnapriya, K., Loveleen, Chauhan, S. and Solanki, S. S., Analyzing the melodic structure of a north indian raga: a statistical approach. Electron. J. Musicol., 2009, XII.
- Bhatkhande, V. N., Hindustani Sangeet Paddhati Kramik Pustak Malika, Sakhi Prakashan, New Delhi, 1990.
- Norden, E. H. et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A Math. Phys. Eng. Sci., 1998, 454(1971), 903–995.
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