Nonlinear characteristics of music signals based on chaos theory

PDF(687 KB)

Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (3) : 39-43.

ZHAO Zhicheng , FANG Lixian

Author information +

History +

Abstract

Music signals are an important form for people to express their feelings and communicate each other.A system to produce music signals is a nonlinear dynamic one with time delay.It is difficult to analyze nonlinear characteristics of music signals with the tradition means.Here, a music signal was divided into parts with the section of a musical composition, local characteristics of a music signal were analyzed and then its whole characteristics were summarized and speculated.Through calculations, the power spectrum and Lyapunov exponent of a music signal were analyzed.The results showed that the music signal has weak chaotic characteristics; the music signal has a complex internal structure after the correlation dimension calculation; classic piano pieces have more consistent features and their internal structures are more complex compared with those of Disco and other kinds of music; the nonlinear characteristics of music signals are stable after the correlation dimension calculation with the definite difference method.

Key words

Chaos theory / Lyapunov index / Correlation dimension / Nonlinear characteristics

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

ZHAO Zhicheng,FANG Lixian . Nonlinear characteristics of music signals based on chaos theory[J]. Journal of Vibration and Shock, 2019, 38(3): 39-43

References

[1] Sanyal S, Banerjee A, Pratihar R, et al. Detrended Fluctuation and Power Spectral Analysis of alpha and delta EEG brain rhythms to study music elicited emotion[C]. International Conference on Signal Processing, Computing and Control. IEEE, 2016:205-210.
[2] Thayer R E, Newman J R, Mcclain T M. Self-regulation of mood: Strategies for changing a bad mood, raising energy, and reducing tension.[J]. Journal of Personality & Social Psychology, 1994, 67(5):910-910.
[3] 胡海岩，王在华. 非线性时滞动力系统的研究进展[J].力学进展，1999,29(4) :501-512
Hu Hai-yan, Wang Zai-hua. Review on nonlinear dynamic systeams involving time delays[J] . Advances in Mechanics, 1999, 29(4) : 501-512
[4] 黄宗权. 音乐中的线性与非线性研究——对乔纳森•克拉默音乐时间新观念的哲学美学考察[J]. 黄钟, 2013(3):114-125. Huang Z Q. Research in the Linearity and Nonlinearity of the Music-An Inspection of Jonathan Kramer’s New Concept on Musical Time by Philosophy and Aesthetics Principle [J]. Huangzhong, 2013.
[5] Roh T, Hong S, Cho H, et al. A 259.6 μW HRV-EEG Processor With Nonlinear Chaotic Analysis During Mental Tasks[J]. IEEE Transactions on Biomedical Circuits & Systems, 2016, 10(1):209-218.
[6] 韦岗，陆以勤，欧阳景正. 混沌、分形理论与语音信号处理[J].电子学报，1996,24(1)34-38
Wei Gang, Lu Yi-qing, Ouyang Jing-zheng.Chaos and Fractal Theories for Speech Signal Processing[J]. Acta Electronica Sinica，1996：24(1)34-38
[7] He S, Sun K, Wang H. Multivariate permutation entropy and its application for complexity analysis of chaotic systems[J]. Physica A Statistical Mechanics & Its Applications, 2016, 461:812-823.
[8] Grassberger P,et al. Characterization of Strange Attractors [J]. Physical Review Letters, 1983,50(5):346-349
[9] Packard N H, Crutchfield J P, Farmer J D, et al. Geometry from a time series[J]. Physical Review Letters, 1980, 45(9):712-172.
[10] 许岩. 含噪混沌时间序列相空间重构参数估计[D]. 重庆大学, 2013.
Xu Yan. Estimating Parameters in Phase Space Reconstruction of Noisy Chaotic Time Series[D]. Chongqing University,2013
[11] Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series[J]. Physica D Nonlinear Phenomena, 1985, 16(3):285-317.
[12] 宋克歆. 基于分形理论视野下的传统曲式研究——以三部性结构为例[D]. 江苏师范大学, 2014.Song Kexin. The traditional music based on Fractal Theory——in the case of Tri-part form [D]. JiangSu Normal University, 2014
[13] Feltekh K, Jemaa Z B, Fournier-Prunaret D, et al. Border collision bifurcations and power spectral density of chaotic signals generated by one-dimensional discontinuous piecewise linear maps[J]. Communications in Nonlinear Science & Numerical Simulation, 2014, 19(8):2771-2784.