基于混沌理论的音乐信号非线性特征研究

Nonlinear characteristics of music signals based on chaos theory

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。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。

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.