分形理论下基于时间序列的音乐识别研究

Music recognition using time series based on the fractal theory

将分形理论和时间序列(混沌序)运用与音乐信号识别,为音乐领域的智能发展提供实验依据.首先对分形理论进行质性分析,并且提出关联维数算法,判断音乐分形程度.接着提出音乐中混沌现象的特征.最后进行实际音乐的实验分析,以钢琴曲目《致爱丽丝》、流行音乐《Discotheque》和哀乐为例,对3种曲目进行材料性质分析,分析不同曲目的Lyapunov指数(判断时间序列)和关联维数(判断分形程度).结果表明:3种曲目在不同阶数下的关联维数基本没有改变,说明不同曲目信号内的分形程度具有稳定性.

This research aims to apply the fractal theory and time series(chaotic order)to music signal recognition and provide an experimental basis for intelligent development in music studies.First,the fractal theory used is analyzed qualitatively,and a correlation dimension algorithm is proposed to judge the fractal degree of music.Second,the characteristics of chaos in music are put forward.Finally,the actual music is experimentally analyzed.The piano music(For Elise),Discotheque,and funeral music are taken as examples,their material properties are analyzed,and the Lyapunov exponent(judging time series)and correlation dimension(judging the fractal degree)of different musical performances are analyzed.The results show thattheir correlation dimension has no change in different orders,which indicates that the fractal degree of different tracks is stable.