基于混沌理论的音乐信号非线性特征研究

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (3) : 39-43.

论文

基于混沌理论的音乐信号非线性特征研究

赵志成,方力先

作者信息 +

Nonlinear characteristics of music signals based on chaos theory

ZHAO Zhicheng , FANG Lixian

Author information +

文章历史 +

摘要

音乐信号是人们表达情感与交流的重要形式，其实际是一个时滞的非线性动力学系统，用传统手段难以分析音乐信号的非线性特征。本文根据音乐的曲式结构中的小节对音乐信号进行划分，分析音乐信号局部特征并由此总结推测其整体特征。通过计算分析音乐信号的功率谱和李雅普诺夫指数，验证音乐信号具有弱混沌特性。其关联维数的计算结果表明音乐信号具有复杂的内部结构，且经典钢琴曲有较一致的特征，对比Disco等乐曲，其内部结构更复杂。对音乐信号差分运算后的关联维数计算结果，证明了其非线性特征具有稳定性。

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.

导出引用

赵志成,方力先. 基于混沌理论的音乐信号非线性特征研究[J]. 振动与冲击, 2019, 38(3): 39-43

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

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