Research On Time-frequency Analysis Based On Sparse Fast Fourier Transform

Time-frequency analysis is a common method of non-stationary signals processing.Fourier transform as the basic unit of time-frequency analysis,its efficiency seriously affects the later.According to the present research,most scholars focus on the improvement of time or frequency resolution,few of them pay their attention to the promotion of time-frequency execution.Compare with the fast Fourier transform(FFT),the sparse Fourier transform is more efficient.But the sparse Fourier transform is seldomly used in time-frequency analysis in existing literature.Thus,this thesis focuses on two kinds of sparse Fourier transform algorithms and using them in time-frequency analysis to replacing traditional FFT.The feasibilities,efficiencies and limitions of the time-frequency analysis based on sparse Fourier transform are verified by theoretical analysis and simulation.Firstly,the research status of time-frequency analysis and sparse Fourier transform are discussed.Secondly,the basic principles of short-time Fourier transform,Wigner-Ville distribution and S transform are introduced.The strengths and weaknesses of these three kinds of time-frequency analysis are analyzed to obtain the theoretical supports of sparse Fourier transform based time-frequency analysis.Thirdly,a hash algorithm based sparse Fourier transform(SFFT)is studied.In order to realize the sparse Fourier transform of the signal whose sparsity is unknown,an adaptive sparse Fourier transform is proposed.Sparse fast Fourier transform based time-frequency analysis is acquired by replacing fast Fourier transform with sparse fast Fourier transform in short-time Fourier transform,Wigner-Ville distribution and S transform.The feasibilities of sparse fast Fourier transform based short-time Fourier transform and Wigner-Ville distribution are proved.Compared with the conventional short-time Fourier transform,the sparse fast Fourier transform based short-time Fourier transform is more efficient.Fourthly,the fast Fourier aliasing-based sparse transform(FFAST)is researched.Its main idea is the utilizing of the signal downsampling property and shifting property.Through these two properties,the aliasing codes are acquired.By the decoding of these aliasing codes,the fast Fourier aliasing based sparse transform algorithm can be realized.The FFT in short-time Fourier transform and Wigner-Ville distribution are substituted by FFAST in order to achieve the time-frequency analysis based on FFAST.Simulation results show that FFAST based short-time Fourier transform and Wigner-Ville distribution are feasible.Compare with the SFFT based short-time Fourier transform,the FFAST based short-time Fourier transform is more efficient.In the end,the research works of this thesis are summarized.The deficiencies of the works are analyzed to giving the later researchers directions.