Improvement Of Fourier Transform Algorithm In Algebraic Signal Processing

Algebra signal processing is developed on the basis of linear signal processing.In 2008,Markus Puschel and Jose M.F.Moura proposed the theoretical framework of algebra signal processing,gave one-dimensional time signal model and the related concepts of signal processing in the model.For example,filtering,spectral decomposition,frequency response and Fourier transform.In 2012,Aliaksei and Sandryhaila established new signal model through redefining time shift of the signal model and gave Fourier transform,filtering and spectral decomposition concept of new signal model.In 2015,Pablo Soto processed the Fourier transform matrix of one-dimensional time signal model,which can reduce the time complexity by using the sparse matrix.In this paper,the improved signal model is proposed by changing the boundary conditions of signal model and the improved Fourier transform is given.The main research work is as follows:(1)Introduce the algebra signal processing theory,the Fourier transform and the real Fourier transform of classical one-dimensional finite time signal model.Extracting the frequency information of the sinusoidal signal containing noise by using Fourier transform algorithm of the model.The simulation experiment shows that the Fourier transform algorithm of the model can accurately extract the frequency information of the sinusoidal signal under a certain range of noise intensity.(2)By changing the boundary conditions of classical one-dimensional finite time signal model,this paper gives a new kind of boundary condition,and then obtains an improved signal model.At the same time,the Fourier transform and the real Fourier transform of improved signal model are given.Extracting the frequency information of the sinusoidal signal containing noise by using Fourier transform algorithm of the improved model.The simulation experiment shows that the Fourier transform algorithm of the improved signal model can also accurately extract the frequency information of the sinusoidal signal under a certain range of noise intensity.(3)This paper gives the improved Fourier transform based on Cooley-Tukey algorithm in the improved signal model,which can reduce the time complexity by using the sparsematrix The simulation experiment shows that the improved Fourier transform based on Cooley-Tukey algorithm can extract the frequency information of the sinusoidal signal under the strong noise background.