Sparse Fractional Fourier Transform And Its Applications In Exploration

Many challenging engineering applications can be formulated as non-stationary signal analysis problems in the transform domain.By projecting the signals onto a basis of linear chirps,the discrete fractional Fourier transform(DFrFT)is a powerful signal processing tool that suitable for analyzing such signals.However,the additional free order parameter requires a much higher computational complexity than the conventional discrete Fourier transform,and the situation gets even worse when a large-scale data set with an unknown optimum rotation angle is to be processed.Thus,an efficient computation method is needed to facilitate the applications of DFrFT.On the other hand,accurately and efficiently estimating the parameters of the linear frequency modulated(LFM)signals with strong interferences and an extremely low input signal-to-noise ratio is one of the important tasks in many application scenarios,especially in exploration fields.The presence of cross-terms between multi-components and the high computation burden are also two conundrums to solve.In this context,a novel probabilistic numeric algorithm is proposed to reduce the computational complexity of DFrFT,and a fast parameter estimation scheme for LFM signals is also presented.Extensive simulations and application examples are provided to illustrate the effectiveness of the proposed approaches.The main contributions of this dissertation are summarized as follows:1.Sparse fractional Fourier transform(SFrFT)is proposed.Most practical signals in nature exhibit sparsity in fractional Fourier domain.By exploiting this property,SFrFT is proposed based on Pei's sampling type algorithm to substantially reduce the computational complexity when dealing with large data sets that are sparse in the fractional domain,and this algorithm does not need a priori knowledge of the the sparsity pattern.The simulation results demonstrate the satisfactory multi-component resolution performance and robustness to noise.On the basis of the proposed algorithm,a sparse fractional cross ambiguity function algorithm and a sparsity-based fast acquisition approach are developed,which are then applied to the coherent integration of accelerating targets in passive bistatic radar and the synchronization of high dynamic direct-sequence spread-spectrum signals.Both high target acceleration and high dynamic scenario manifest in the form of acute variation of the Doppler frequency in the signal phase,thus,the sparsity of signal in the fractional Fourier domain is utilized to concentrate the signal energy and improve the detection probability in real time.2.A fast LFM parameter estimation approach is proposed for weak signals that are sparsely represented in the fractional Fourier domain.A novel algorithm that combines segmented discrete polynomial-phase transform(DPT)and SFrFT is proposed to first segment the input signals to perform fast-time coherent integration in order to mitigate the impact of the low input SNR on the algorithm performance.Then,slow-time DPT is conducted to obtain a coarse estimation of the chirp rates.To eliminate the effect of cross-terms and achieve a finer estimation of the parameters,the SFrFT is applied to the original input signal with different rotation angles,and the chirp rates and the initial frequencies are determined by peak detection with a decision threshold.The proposed approach yield a significant reduction of the computational load with a satisfactory multi-component estimation performance.As a practical application example,a fast and accurate radar-based fractional Fourier domain automatic human fall detection scheme is presented.Compare with the conventional time-frequency analysis approaches,the proposed method achieves higher signal energy concentration and thus yields improved fall detection in low signal-to-noise ratio scenarios.3.A detection scheme for weak astronomical signals with missing samples and strong frequency-hopping(FH)interferences is proposed.The boom in wireless technology innovation has led to an increasingly conspicuous radio frequency spectrum congestion.As a result,the bandwidth traditionally slated for radio telescopes is now facing undesired frequency infringement,which may interfere with reception and interpretation of astronomical data.In this context,a combined interference mitigation and weak astronomical signal detection scheme is developed to achieve the coexistence of wireless transmitters and radio telescopes.In particular,FH communication signal as a selected source of interference is investigated.In the framework of bilinear time-frequency joint-variable representation,to yield an improved spectrum estimation capability,a Bayesian compressive sensing based method is proposed to exploit the structures of the FH signals,missing sample induced artifacts and cross terms through proper prior and kernel designs.The FH interferences are removed according to the estimated FH spectrum,then the weak astronomical signals are detected using the aforementioned fast LFM parameter estimation approach.