Using Nonlinear Diffusion Model to Identify Music Signals

Abstract

In this paper, combined with the partial differential equation music signal smoothing model, a new music signal recognition model is proposed. Experimental results show that this model has the advantages of the above two models at the same time, which can remove noise and enhance music signals. This paper also studies the music signal recognition method based on the nonlinear diffusion model. By distinguishing the flat area and the boundary area of the music signal, a new diffusion coefficient equation is obtained by combining these two methods, and the corresponding partial differential equation is discretized by the finite difference method with numerical solution. The application of partial differential equations in music signal processing is a relatively new topic. Because it can accurately model the music signal, it solves many complicated problems in music signal processing. Then, we use the group shift Fourier transform (GSFT) to transform this partial differential equation into a linear homogeneous differential equation system, and then use the series to obtain the solution of the linear homogeneous differential equation system, and finally use the group shift inverse Fourier transform to obtain the noise frequency modulation time-dependent solution of the probability density function of the interference signal. This paper attempts to use the mathematical method of stochastic differentiation to solve the key problem of the time-dependent solution of the probability density function of noise interference signals and to study the application of random differentiation theory in radar interference signal processing and music signal processing. At the end of the thesis, the application of stochastic differentiation in the filtering processing of music signals is tried. According to the inherent self-similarity of the music signal system and the completeness and stability of the empirical mode decomposition (EMD) algorithm, a new kind of EMD music using stochastic differentiation is proposed for signal filtering algorithm. This improved anisotropic diffusion method can maintain and enhance the boundary while smoothing the music signal. The filtering results of the actual music signal show that the algorithm is effective.