| Non-stationary signal exits widely in the nature. A lot of typical signals possess non-stationary property in the national economic and military fields. It can be said that studies on non-stationary signal processing technologies has become one of the most basic and important tasks in signal processing subject.As a generalized form of conventional Fourier transform, FrFT is essentially a unified time-frequency representation. Compared with other time-frequency analysis tools, FrFT has definite physical meaning, unified description method, excellent mathematical property and efficient discrete algorithm, which is applied widely in radar, communication, geological exploration and biomedical engineering. Based on theories of FrFT, this paper studied deeply on multi-component signal parameter estimation, wideband array signal processing and time-frequency filter designing. The main innovations are summarized as follows:To estimate the parameters of LFM signals precisely in noisy environment, an estimation method based on FrFT and spectrum correction is presented. This method converts the estimation to 2-d spectral peak searching, and the energy centrobaric correction is introduced, which realizes the super-resolution estimation of spectral peak without increasing any computational cost. On this basis, a 1-d correction method is proposed based on RAT and FrFT. This method reduces the 2-d peak searching to two 1-d corrections, which reduce the complexity substantially. Finally, the estimation precision under white Gaussian noise is analyzed, and the efficiency of the method is verified.Current DOA estimation algorithm for wideband LFM signals can be applied only to regular array. To solve this problem, an estimation method based on FrFT is proposed. Based on the energy-concentrated property of LFM signal in fractional Fourier domain, a new array data model is constructed, then the DOAs can be estimated by spectral searching over spatial function. It is verified that this estimator is generalized form of conventional FrFT-ESPRIT method. Simulation experiments are also conducted.According to partly calibrated array, a 2-d DOA estimation method is proposed. The incident signals are sampled in spatial and time domain synchronously, and a new time-frequency spatial DOA matrix is constructed, then the DOAs can be estimated by eigen-decomposition processes. This method has lower constraint of array structure, and can be applied to partly calibrated array with arbitrary structure.A DOA estimation method for coherent LFM signals is proposed. Based on the dechirping property of LFM signal in a certain domain, a new array data model is constructed, then the matrix reconstruction and MUSIC algorithm are used to estimate the DOAs of signals. If there are multiple groups of coherent signals, separate them in different energy-concentrated domains first, then carry the estimation on each of the groups. This method has better resolution and anti-noise performance, which has extensive application prospect.To realize signal restoration in complicated noise, a design method of fractional Fourier domain filter is proposed. The signal distribution is obtained by GT, and based on the image segmentation and SVM classification, regions on time-frequency plane are separated, then the filter parameters can be determined by separating line. For linearly inseparable case, the piecewise linear fitting is performed, then the parallel filter banks are constructed from the fitting equation. This method realizes the global optimization of filter parameters, and needs no prior knowledge, which can meet the reliable and general requirements simultaneously.The applications of time-frequency filter are studied. The proposed filter is applied to SAR multiple moving targets imaging and WD cross-term suppression. The implementation flow is given. The improvement measures for different environment are analyzed. Simulation experiments are conducted to analyze the efficiency of the method.
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