Underdetermined DOA estimation and blind separation of non-disjoint sources in time-frequency domain based on sparse representation method

This paper deals with the blind separation of nonstation-ary sources and direction-of-arrival （DOA） estimation in the under-determined case, when there are more sources than sensors. We assume the sources to be time-frequency （TF） disjoint to a certain extent. In particular, the number of sources presented at any TF neighborhood is strictly less than that of sensors. We can identify the real number of active sources and achieve separation in any TF neighborhood by the sparse representation method. Compared with the subspace-based algorithm under the same sparseness assumption, which suffers from the extra noise effect since it can-not estimate the true number of active sources, the proposed algorithm can estimate the number of active sources and their cor-responding TF values in any TF neighborhood simultaneously. An-other contribution of this paper is a new estimation procedure for the DOA of sources in the underdetermined case, which combines the TF sparseness of sources and the clustering technique. Sim-ulation results demonstrate the validity and high performance of the proposed algorithm in both blind source separation （BSS） and DOA estimation.

Novel Time-frequency Analysis and Representation of EEG

A novel method of EEG time-frequency analysis and representation based on a wavelet network is presented. The wavelet network model can represent the EEG data effectively. Based on the wavelet network model, a novel time-frequency energy distribution function is obtained, which has the same time-frequency resolution as Wigner-Ville distribution and is free of cross-term interference. There is a great potential for the use of the novel time-frequency representation of nonstationary biosignal based on a wavelet network in the field of the electrophysiological signal processing and time-frequency analysis.

Application of Local Wave Time-Frequency Spectrum and Neural Networks to Fault Classification in Rotating Machine

A new method of fault analysis and detection by signal classification inrotating machines is presented. The Local Wave time-frequency spectrum which is a new method forprocessing a non-stationary signal is used to produce the representation of the signal. This methodallows the decomposition of one-dimensional signals into intrinsic mode functions (IMFs) usingempirical mode decomposition and the calculation of a meaningful multi-component instantaneousfrequency. Applied to fault signals , it provides new time-frequency attributes. Then the momentsand margins of the time-frequency spectrum are calculated as the feature vectors. The probabilisticneural network is used to classify different fault modes. The accuracy and robustness of theproposed methods is investigated on signals obtained during the different fault modes (early rub,loose, misalignment of the rotor).

Sparse time-frequency representation of nonlinear and nonstationary data Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data. These methods are inspired by the empirical mode decomposition method （EMD） and the recently developed compressed （compressive） sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a（t） cos（0（t））}, where a is assumed to be less oscillatory than cos（θ（t）） and θ ＇≥ 0. This problem can be formulated as a nonlinear ι0 optimization problem. We have proposed two methods to solve this nonlinear optimization problem. The first one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit. Convergence analysis has been carried out for the nonlinear matching pursuit method. Some numerical experiments are given to demonstrate the effectiveness of the proposed methods.

A two-level method for sparse time-frequency representation of multiscale data Dedicated to Professor LI TaTsien on the Occasion of His 80th Birthday

Based on the recently developed data-driven time-frequency analysis(Hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we first run a local algorithm to get a good approximation of the instantaneous frequency. We then pass this instantaneous frequency to the global algorithm to get an accurate global intrinsic mode function(IMF)and instantaneous frequency. The two-level method alleviates the difficulty of the mode mixing to some extent.We also present a method to reduce the end effects.

基于自适应最优抛物线核函数的Wigner-21/2维时频表示算法

针对低信噪比条件下非平稳、非线性和非高斯信号的时频特征分析,提出了一种基于自适应最优抛物线核函数的Wigner-212维时频表示算法.采用依赖于特定时频点的二维时频局部模糊函数替代传统Cohen类高阶时频分析中通用的全局时频模糊函数;利用自适应核处理技术获得局部模糊函数的最佳抛物线核函数,以最大限度地抑制交叉项的影响,提高算法的时频分辨率和信号自适应性;通过合成信号和水声信号的仿真实验进行时频分析,并与现有时频算法加以对比.结果表明,在低信噪比条件下,所提出算法对瞬态信号的检测优势明显,能够取得优良的时频特征解析效果.

基于自适应最优核时频分布理论的ISAR成像方法

由于运动的复杂性,传统的成像方法已无法满足机动目标成像的要求。在分析机动目标复杂运动引起目标回波多普勒相位非线性变化的基础上,提出了一种基于自适应最优核时频分布(AOK TFR)理论的ISAR成像方法。通过计算回波数据不同距离单元的AOK TFR,得到不同时刻目标的瞬态ISAR像,且不受交叉项的影响;通过估计距离单元的瞬时多普勒频率并依此对成像时间段进行选择。仿真数据结果验证了该方法的有效性。

基于EM算法的最优斜高斯核设计

对于采用固定窗或核的时频分布,其适用的信号形式具有很大的局限性。基于信号的核能克服这样的缺点,斜高斯核是其中一类,为了得到基于不同信号的最优斜高斯核,本文提出采用EM算法根据实际信号的模糊函数估计斜高斯核的参数,以达到核的最优设计。

Research on LPI radar signal detection and parameter estimation technology

Modern radar signals mostly use low probability of intercept(LPI)waveforms,which have short pulses in the time domain,multicomponent properties,frequency hopping,combined modulation waveforms and other characteristics,making the detection and estimation of LPI radar signals extremely difficult,and leading to highly required significant research on perception technology in the battlefield environment.This paper proposes a visibility graphs(VG)-based multicomponent signals detection method and a modulation waveforms parameter estimation algorithm based on the time-frequency representation(TFR).On the one hand,the frequency domain VG is used to set the dynamic threshold for detecting the multicomponent LPI radar waveforms.On the other hand,the signal is projected into the time and frequency domains by the TFR method for estimating its symbol width and instantaneous frequency(IF).Simulation performance shows that,compared with the most advanced methods,the algorithm proposed in this paper has a valuable advantage.Meanwhile,the calculation cost of the algorithm is quite low,and it is achievable in the future battlefield.

Continuous frequency and phase spectrograms: a study of their 2D and 3D capabilities and application to musical signal analysis

A new lighting and enlargement on phase spectrogram （PS） and frequency spectrogram （FS） is presented in this paper. These representations result from the coupling of power spectrogram and short time Fourier transform （STFT）. The main contribution is the construction of the 3D phase spectrogram （3DPS） and the 3D frequency spectrogram （3DFS）. These new tools allow such specific test signals as small slope linear chirp, phase jump case of musical signal analysis is reported. The main objective is to and small frequency jump to be analyzed. An application detect small frequency and phase variations in order to characterize each type of sound attack without losing the amplitude information given by power spectrogram

Testing for Nonlinearity in Dynamic Characteristics of Vertical Upward Oil-Gas-Water Three-phase Bubble and Slug Flows

Based on the conductance fluctuation signals measured from vertical upward oil-gas-water three-phase flow experiment, time frequency representation and surrogate data method were used to investigate dynamical characteristics of oil-in-water type bubble and slug flows. The results indicate that oil-in-water type bubble flow will turn to deterministic motion with the increase of oil phase fraction f o and superficial gas velocity U sg under fixed flowrate of oil-water mixture Q mix . The dynamics of oil-in-water type slug flow becomes more complex with the increase of U sg under fixed flowrate of oil-water mixture. The change of f o leads to irregular influence on the dynamics of slug flow. These interesting findings suggest that the surrogate data method can be a faithful tool for characterizing dynamic characteristics of oil-in-water type bubble and slug flows.

An Improved Chirplet Transform and Its Application for Harmonics Detection

The chirplet transform is the generalization form of fast Fourier transform , short-time Fourier transform, and wavelet transform. It has the most flexible time frequency window and successfully used in practices. However, the chirplet transform has not inherent inverse transform, and can not overcome the signal reconstructing problem. In this paper, we proposed the improved chirplet transform (ICT) and constructed the inverse ICT. Finally, by simulating the harmonic voltages, The power of the improved chirplet transform are illustrated for harmonic detection. The contours clearly showed the harmonic occurrence time and harmonic duration.

Scattering center modeling for low-detectable targets

The scattering centers(SCs)of low-detectable targets(LDTs)have a low scattering intensity.It is difficult to build the SC model of an LDT using the existing methods because these methods mainly concern dominant SCs with strong scattering contributions.This paper presents an SC modeling approach to acquire the weak SCs of LDTs.We employ the induced currents at the LDT to search SCs,and the joint time-frequency transform together with the Hough transform to separate the scattering contributions of different SCs.Particle swarm optimization(PSO)is applied to improve the estimation results of SCs.The accuracy of the SC model built by this approach is verified by a full-wave numerical method.The validation results show that the SC model of the LDT can precisely simulate the signatures of high-resolution images,such as high-resolution range profile and inverse synthetic aperture radar(ISAR)images.

A fast time-frequency response based differential spectral energy protection of AC microgrids including fault location

This paper proposes a pattern recognition based differential spectral energy protection scheme for ac microgrids using a Fourier kernel based fast sparse time-frequency representation(SST or simply the sparse S-Transform).The average and differential current components are passed through a change detection filter,which senses the instant of fault inception and registers a change detection point(CDP).Subsequently,if CDP is registered for one or more phases,then half cycle data samples of the average and differential currents on either side of the CDP are passed through the proposed SST technique,which generates their respective spectral energies and a simple comparison between them detects the occurrence and type of the fault.The SST technique is also used to provide voltage and current phasors and the frequency during faults which is further utilized to estimate the fault location.The proposed technique as compared to conventional differential current protection scheme is quicker in fault detection and classification,which is least effected from bias setting,has a faster relay trip response(less than one cycle from fault incipient)and a better accuracy in fault location.The significance and accuracy of the proposed scheme have been verified extensively for faults in a standard microgrid system,subjected to a large number of operating conditions and the outputs vindicate it to be a potential candidate for real time applications.

Chirplet Signal and Empirical Mode Decompositions of Ultrasonic Signals for Echo Detection and Estimation

In this study, the performance of chirplet signal decomposition (CSD) and empirical mode decomposition (EMD) coupled with Hilbert spectrum have been evaluated and compared for ultrasonic imaging applications. Numerical and experimental results indicate that both the EMD and CSD are able to decompose sparsely distributed chirplets from noise. In case of signals consisting of multiple interfering chirplets, the CSD algorithm, based on successive search for estimating optimal chirplet parameters, outperforms the EMD algorithm which estimates a series of intrinsic mode functions (IMFs). In particular, we have utilized the EMD as a signal conditioning method for Hilbert time-frequency representation in order to estimate the arrival time and center frequency of chirplets in order to quantify the ultrasonic signals. Experimental results clearly exhibit that the combined EMD and CSD is an effective processing tools to analyze ultrasonic signals for target detection and pattern recognition.

基于循环自相关/平均幅度差函数的弹道目标微动周期估计

雷达微多普勒(m-D)是弹道目标的突出特征,为弹头识别提供了重要手段。然而,当弹道目标的微动伴随平动时,时频分布不再表现为正弦调制曲线,此时基于时频分布正弦假设的微多普勒特征提取方法可能失效。针对这一问题,提出了一种循环自相关函数(CACF)和循环平均幅度差函数(CAMDF)相结合的估计算法,来获取时频分布的循环系数矩阵和该矩阵的平均循环系数,从而估计出弹道目标的微动周期。该算法以时频分布的循环周期性代替正弦调制的周期性,不需要假设目标平动已被准确补偿,有效克服了传统微动周期估计方法的不足。理论推导论证了该算法的可行性,仿真实验验证了该算法的有效性和抗噪性。

Scattering Center Modeling Using Adaptive Segmental Compressive Sampling

In order to deal with aliasing distortions of Doppler frequencies shown in time-frequency representation（ TFR） with aspect undersampling,an approach using adaptive segmental compressive sampling according to the aspect dependencies of the scattering centers is proposed. The random noise problem induced by compressive sampling is solved by employing a series of signal processing techniques of filtering,image transformation and Hough Transform. Three examples are presented to verify the effectiveness of this approach. The comparisons between the built models and the precise scattered fields computed by a well-validated full-wave numerical method are investigated,and the results showgood agreements between each other.

Subspaces of FM^mlet transform

The subspaces of FMmlet transform are investigated. It is shown that some of the existing transforms like the Fourier transform, short-time Fourier transform, Gabor transform, wavelet transform, chirplet transform, the mean of signal, and the FM-1let transform, and the butterfly subspace are all special cases of FMmlet transform. Therefore the FMmlet transform is more flexible for delineating both the linear and nonlinear time-varying structures of a signal.

Interception Algorithm of S-cubed Signal Model in Stealth Radar Equipment

Radar equipment of stealth platforms such as aircraft have adopted the newest modem technology to design the signal waveforms. One of the important and effective methods is the hybrid waveform called spread spectrum stretch （S-cubed） which combines linear frequency modulation （LFM） and discrete phase code. In order to investigate the function of enemy＇s stealth radar equipment, the interception algorithm of S-cubed is needed. In this paper, a novel detection and parameter estimation approach for the reconnaissance S-cubed radar signal is presented. First, the generalized time-frequency representation of Zhao, Atlas, and Marks （ZAM-GTFR） and Hough transforms （HT） are applied to detecting the signal, and then the initial frequency and modulation slope of LFM are estimated from the ZAM-GTFR. On the basis of LFM information, the reconstructing signal is generated. Finally, the code rate of discrete phase code is extracted from the negative peaks of the ZAM-GTFR. Simulation results show that the proposed algorithm has higher estimation accuracy when the signal to noise ratio （SNR） is above 3 dB.

Properties and convergence analysis of FM^mlet transform

The linearity,time shifting,time scaling,and time inversion properties of FMmlet transform are proved,and the frequency shifting property of one of the subspaces of FMmlet transform,namely the chirplet transform is presented.Moreover,it is proved that in the process of FMm let based atomic signal decomposition,the residual signals decay exponentially.