Study On Nonlinear Characteristics Of Musical Signals

Music is not only the common language of human society but also has a very important role in people's lives.Studies have shown that each person has a specific music-sensitive area in his or her brain.When the music reaches the human ear and acts on the brain,it is possible to increase the excitability of some cells,such as nerve cells.These cells will promote the body to produce some useful hormones or enzymes,hormones and enzymes by regulating the secretion of human body fluids,enhance the body's immune capacity and enhance metabolism.This special function of music is determined by the characteristics of the music signal itself.From a particular sense,the music signal can better reflect the movement of the brain nervous system characteristics.However,due to the complexity of the music signal itself,long-term theoretical research foundation is weak.From the system point of view,the music signal is a time delay of nonlinear dynamic system,time-delay systems tend to have multiple degrees of freedom,high-dimensional characteristics.Therefore,the application of non-linear method to study the music signal can reveal the essential laws.The research of this project is based on different types of music signals,such as classical piano music,disco and sad music.The first step is to remove the noise in the music,the second step is to divide the music signal by section.The size of the Lyapunov exponent is used to judge whether the music signal is chaotic.The non-linear characteristic of the music signal is determined by calculating the size of the correlation dimension.The difference method is used to calculate the difference of the music signal,and then calculate the correlation dimension of the music signal after the difference method.The main contents and achievements of this paper are as follows:(1).Through reading and experiments,a new music signal division method is determined.According to the music form can be resolved in the section as the basis for the division.(2).Signal spectrum analysis method is the superposition of Random phase and periodic oscillation signals.In the spectrum structure,if the signal has a continuous power spectrum is to prove that the signal has a chaotic phenomenon.In the study,we found that the power spectrum of the music signal has the above characteristics,so we can judge the music signal has the characteristics of chaos.(3).The Lyapunov exponent is an important index to judge whether the system has chaotic characteristics.If the system has positive Lyapunov exponent,we can prove that the system is chaotic.The Lyapunov exponent of the selected music signal is greater than zero,which indicates that the music signal has chaotic characteristics,and the Lyapunov exponent is small,which indicates that the Lyapunov exponent is controlled and orderly.(4).The correlation dimension is an important parameter describing the degree of fractal complexity,and it can describe the complexity of things.By calculating the correlation dimension of five different kinds of music signals,it is found that the correlation dimension fluctuation of the piano signal is the largest,which indicates that the nonlinear characteristic of the piano signal is stronger than other types.This is also consistent with the characteristics of the music itself,because the piano creation is very complex,especially the classic piano.The creation of the piano has high requirements for composer.(5)It is found that the correlation dimension of the music signal does not change with the difference order,which indicates that the nonlinear characteristic is fixed in the music signal and has certain stability...