Time-Frequency Analysis System And Its Application

Time-frequency (TF) analysis has experienced a number of qualitative and quantitative changes during the last three decades, and has gradually received growing attention and further applications in a variety of fields. However, most traditional signal processing methods, developed under rigorous mathematical rigor, are based on linear and stationary assumptions. As the data from the real world are generally neither linear nor stationary, the traditional data analysis methods aiming at linear and stationary signals and processes are becoming glaringly inadequate. This paper introduces several TF methods, aiming at nonlinear and nonstationary signals, such as short time Fourier transform (STFT), Cohen's class of TF distributions, Hilbert-Huang transform (HHT), improved HHT with wavelet package transform, Hilbert spectrum via maximal-overlap discrete wavelet packet transform (MODWPT) and multitaper reassigned spectrum (MRS). The errors of Empirical Mode Decomposition (EMD) with different interpolation function and different sample frequency are also discussed. Furthermore, we also analyzed the performance measure of separation for two-tones signal of EMD. Effects of different signal length and sifting number on the statistical properties of IMFs produced by EMD of Gaussian white noise are studied and the obtained results show that the probability density functions of IMFs are non-Gaussian in most case. Under the circumstance of small signal length and small sifting number, the distributions of IMFs are more Laplacian than Gaussian, while in the case of large signal length and high number of iterations, it appears multimodal distributions in all IMFs.The performances of frequency separating ability and TF resolution of five TF methods are comprehensively compared using several examples including single and multicomponent chirp signals in the presence of noise or noise free. Effectiveness measure by Renyi entropy and error measure concerned with a bandpass filtered white Gaussian noise is implemented for comparison of each algorithm. The applicabilities of five methods in analyzing three typical nonlinear systems are illustrated. The results show that MRS is most suitable for nonstationary signal analyzing. Otherwise, the signalment of nonlinear signal using HHT is most precise and comprehensive.For the purpose of using different TF methods seperatively for nonlinear signals and nonstationary signals, this paper introduces a TF analysis system that we designed and implemented based on MATLAB. We also embedded nonlinearity test and stationarity test modules in our system. The pretreatment module contains nonlinearity test and stationarity test as well as several common tools for signal processing. In the TF analysis module, our system provides TF algorithms of many kinds. The user can set the system parameters of different TF algorithms according to their need. The system has a user-friendly interface which provides custom messages of abnormal input and detailed document of instructions. It was designed for easy operating, being used as a convenient and highly customizable toolset for experimenting, teaching and researches. The part of EMD module was already utilized in engineering by China Ship Scientific Research Center.