Research On Multi-attribute Signal Analysismethod Based On Tensor Fourier Transform

With the rapid development of information technology,computer technology and communication technology,signal forms have changed from single to colorful,and various signal forms have emerged,such as video signal,image signal,chemical signal,radar signal,audio signal,gene signal,etc.The signal also develops from one-dimensional signal to high-dimensional signal.Because the multi-dimensional representation of signal reflects the physical meaning of signal in different attribute subspaces,it can feed back more potential structural information between attributes,and tensor,as the expansion of vector and matrix in high-dimensional space,is the natural and essential expression of such high-dimensional signal set,so this paper will use tensor to represent high-dimensional signal.In recent years,tensor analysis is widely used as a multilinear analysis tool.It can process signals with multiple influencing factors,and associate various attributes of signals,including the high-order extended form of signals or signals with multi-dimensional themselves.Therefore,tensor analysis has been widely used in signal processing,artificial intelligence,computer vision and other fields.In the process of signal analysis,many signals only analyze the time zone from the perspective of time domain,with little feedback information.In order to extract more features,it is necessary to transform the signal from time domain to frequency domain through Fourier transform,so as to carry out signal analysis more efficiently.Using Fourier transform,signal denoising and fault detection can be carried out.With the development of science and technology,data sets are also continuously updated,so incremental algorithm is very important for the analysis and processing of multi-attribute data.In this paper,we will study and analyze the multi-attribute signals with more significant features in the frequency domain,extract their frequency-domain features through Fourier transform,and use tensor as the basic representation method of multi-attribute signals.In order to analyze the multi-attribute signals,tensor modeling is carried out for the large-scale and complex multi-attribute signals.The tensor decomposition method is used to extract and analyze the features of multi-attribute signals,summarize the analysis process of multi-attribute signals,and propose a framework that can be applied to multi-attribute signal analysis.This paper analyzes the T-SVD decomposition algorithm,uses Lanczos algorithm to improve the singular value decomposition of matrix in the TSVD decomposition algorithm,and obtains the improved T-SVD decomposition algorithm.The improved algorithm can improve the operation efficiency.Taking bearing fault recognition as an example,the efficiency of the improved algorithm of T-SVD decomposition is verified.The first-order incremental algorithm and the second-order incremental algorithm of the third-order tensor T-SVD decomposition are proposed to improve the computational efficiency.The algorithm is applied to the multi-attribute signal analysis framework proposed in this paper,and the efficiency of the third-order tensor T-SVD decomposition incremental algorithm is verified by taking audio recognition as an example.