On the Use of Spatial Time Frequency Distributions for Signal Extraction

This paper deals with the extraction of signals from their instantaneous linear mixtures using time-frequency distributions. Fundamentally, this problem is a signal synthesis from the time-frequency (t-f) plane. However with the incorporation of the spatial information provided by a multisensor array, the problem can be posed as special case of blind source separation. So far, the blind source separation has been solved using only statistical information available on the source signals. Herein, we propose to solve the aforementioned problem using time-frequency signal representations and the spatial array aperture. The proposed approach relies on the difference in the t-f signatures of the sources to be separated. It is based on the diagonalization of a combined set of spatial time-frequency distribution matrices. A numerical example is provided to illustrate the effectiveness of our method.     

Blind Source Separation in the Time-Frequency Domain Based on Multiple Hypothesis Testing

This paper considers a time-frequency (t-f)-based approach for blind separation of nonstationary signals. In particular, we propose a time-frequency "point selection" algorithm based on multiple hypothesis testing, which allows automatic selection of auto- or cross-source locations in the time-frequency plane. The selected t-f points are then used via a joint diagonalization and off-diagonalization algorithm to perform source separation. The proposed algorithm is developed assuming deterministic signals with additive white complex Gaussian noise. A performance comparison of the proposed and existing approaches is provided.     

基于空间演化谱的Chirp信号极化和DOA的联合估计

本文研究了时变幅度Chirp信号的演化谱,提出了分别在时间轴和频率轴上聚集能量的方法,改善了演化周期谱的能量聚集性。同时,基于时变幅度Chirp信号的空间演化谱,提出了一种新的空间极化时频分布,用此空间极化时频矩阵代替自相关矩阵估计信号子空间和噪声子空间。采用L型正交短偶极子阵列,用ESPRIT算法实现了多Chirp信号DOA和极化参量的联合估计,并提出一种新的多信号参量配对的方法。通过仿真将本文的算法其他一些算法进行了比较。     

Blind source separation based on time-frequency signalrepresentations

Blind source separation consists of recovering a set of signals of which only instantaneous linear mixtures are observed. Thus far, this problem has been solved using statistical information available on the source signals. This paper introduces a new blind source separation approach exploiting the difference in the time-frequency (t-f) signatures of the sources to be separated. The approach is based on the diagonalization of a combined set of “spatial t-f distributions”. In contrast to existing techniques, the proposed approach allows the separation of Gaussian sources with identical spectral shape but with different t-f localization properties. The effects of spreading the noise power while localizing the source energy in the t-f domain amounts to increasing the robustness of the proposed approach with respect to noise and, hence, improved performance. Asymptotic performance analysis and numerical simulations are provided     

基于空间时频分布的宽带源波达方向估计

研究了空间时频分布在宽带阵列处理中的应用。在信号时频特征可分的情况,提出一种新的时频域宽带DoA估计算法,充分利用信号不同的时频特征,结合宽带聚集思想对每个源单独处理得到多个源的DoA估计。该方法具有很好的信号选择性以及抑制干扰和噪声的能力,估计性能优干传统空间时频分布方法。仿真结果验证了新方法的有效性。     

A constrained weighted least squares approach for time-frequencydistribution kernel design

In most applications of time-frequency (t-f) distributions, the t-f kernel is of finite extent and applied to discrete time signals. This paper introduces a matrix-based approach for t-f distribution kernel design. In this new approach, the optimum kernel is obtained as the solution of a linearly constrained weighted least squares minimization problem in which the kernel is vectorial and the constraints form a linear subspace. Similar to FIR temporal and spatial constrained least squares (LS) design methods, the passband, stopband, and transition band of an ideal kernel are first specified. The optimum kernel that best approximates the ideal kernel in the LS error sense, and simultaneously satisfies the multiple linear constraints, is then obtained using closed-form expressions. This proposed design method embodies a well-structured procedure for obtaining fixed and data-dependent kernels that are difficult to obtain using other design approaches     

基于遗传算法和时频分布的跳频信号盲分离

根据跳频信号的非平稳特性,采用一种基于时频分布的跳频信号盲分离算法,通过合理选择符合＂单个自项＂要求的时频点,将盲源分离问题转化成对一组时频分布矩阵联合对角化的数学优化问题,由于遗传算法具有良好的全局寻优能力,因此利用遗传算法对能够表征矩阵联合对交化效果的代价函数进行优化求解,寻找能将矩阵组联合对角化的权矩阵。仿真结果...     

Minimum-variance time-frequency distribution kernels

When dealing with random processes, reduced spectrum estimate variance becomes an important property that augments the list of desirable time-frequency (t-f) distribution properties. In this correspondence, we derive the t-f kernel that satisfies the t-f constraints and provides the minimum variance for the power spectrum estimate for Gaussian white noise processes     

一种新的时频极大似然DOA估计方法

针对非平稳信号,提出一种新的时频域极大似然DOA估计方法,利用参考阵元与阵列中其它阵元输出之间的互伪Wigner-Ville分布建立起时频域的阵列信号模型,通过时频域极大似然方法获得入射方向估计。与基于空间时频分布矩阵的阵列测向方法相比,该方法具有计算量小、交叉项时频分布利用充分的优点。仿真实验证实了该方法的有效性。     

Orthonormal-basis partitioning and time-frequency representation of cardiac rhythm dynamics

Although a number of time-frequency representations have been proposed for the estimation of time-dependent spectra, the time-frequency analysis of multicomponent physiological signals, such as beat-to-beat variations of cardiac rhythm or heart rate variability (HRV), is difficult. We thus propose a simple method for 1) detecting both abrupt and slow changes in the structure of the HRV signal, 2) segmenting the nonstationary signal into the less nonstationary portions, and 3) exposing characteristic patterns of the changes in the time-frequency plane. The method, referred to as orthonormal-basis partitioning and time-frequency representation (OPTR), is validated using simulated signals and actual HRV data. Here we show that OPTR can be applied to long multicomponent ambulatory signals to obtain the signal representation along with its time-varying spectrum.     

脉冲噪声下跳频信号时频图修正

为了在α稳定分布噪声的环境下获得清晰的跳频信号时频图,提出一种基于分数低阶SPWVD(Smoothed Pseudo Wigner-Vile Distribution)与形态学滤波相结合的跳频信号时频图修正算法。首先,根据接收到的多跳频信号建立跳频信号的模型和α稳定分布噪声模型;然后,采用低阶SPWVD变换抑制时频图中脉冲噪声;最后,根据形态学滤波处理方法对残留噪声进一步抑制进而得到清晰时频图。理论分析和仿真结果表明,所提算法在广义信噪比为-5 dB时仍可以得到清晰可靠的跳频信号时频图,并且基于时频图的参数估计性能优良。     

多径传播条件下宽带线性调频信号波达方向估计方法

针对信号出现多径传播情况时现有宽带信号波达方向（direction of arrival, DOA）估计方法性能下降的问题,提出了一种多径传播条件下宽带线性调频（chirp）信号波达方向估计方法,该方法将导向有效投影（steered effective projection, STEP）技术与宽带线性调频信号的时频特性相结合,对具有不同时频特性的信号分量进行分离,逐个处理,并以时频分布矩阵代替传统的协方差矩阵,从而构造有效噪声子空间,实现时域角度估计。本方法无需进行信号聚焦操作,因此理论上不受聚焦误差的影响。仿真结果验证了所提方法的有效性。      

System identification using chirp signals and time-variant filtersin the joint time-frequency domain

We propose a novel method to identify an unknown linear time invariant (LTI) system in low signal-to-noise ratio (SNR) environment. The method is based on transmitting chirp signals for the transmitter and using linear time-variant filters in the joint time-frequency (TF) domain for the receiver to reduce noise before identification. Due to the TF localization property of chirp signals, a large amount of additive white noise can be reduced, and therefore, the SNR before identification can be significantly increased. This, however, cannot be achieved in the conventional methods, where pseudo-random signals are used, and therefore, noise reduction techniques do not apply. Our simulation results indicate that the method proposed outperforms the conventional methods significantly in a low SNR environment. This paper provides a good application of time-frequency analysis and synthesis     

基于时频子空间分解的宽带线性调频信号DOA估计

针对具有时变方向向量的宽带线性调频信号,该文建立了基于短时Wigner-Ville分布(WVD)的空间时频分布矩阵,通过对各个空间时频矩阵的特征分解获得对应的信号子空间和噪声子空间,给出了基于时频子空间投影实现多个时频点综合估计信号DOA的算法。利用空间时频分布的前后向平滑解决了具有相同时频特性信号的均匀线阵DOA估计问题。算法不需要聚汇和插值等复杂的矩阵变换,精度较高,计算简便.仿真实验显示该算法性能显著优越于基于矩阵插值的宽带调频信号DOA估计算法.     

Matched subspace detectors

We formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise. We derive the generalized likelihood ratio (GLR) for each problem in the class. We then establish the invariances for the GLR and argue that these are the natural invariances for the problem. In each case, the GLR is a maximal invariant statistic, and the distribution of the maximal invariant statistic is monotone. This means that the GLR test (GLRT) is the uniformly most powerful invariant detector. We illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise. In each case we give the distribution for the detector and compute performance curves     

CLASSIFICATION OF MPSK SIGNALS USING CUMULANT INVARIANTS

A new feature based on higher order statistics is proposed for classification of MPSK signals, which is invariant with respect to translation(shift),scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise.Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification.Finally, computer simulations and comparisons with existing algorithms are given.     

Wavelet packet feature extraction for vibration monitoring

Condition monitoring of dynamic systems based on vibration signatures has generally relied upon Fourier-based analysis as a means of translating vibration signals in the time domain into the frequency domain. However, Fourier analysis provided a poor representation of signals well localized in time. In this case, it is difficult to detect and identify the signal pattern from the expansion coefficients because the information is diluted across the whole basis. The wavelet packet transform (WPT) is introduced as an alternative means of extracting time-frequency information from vibration signatures. The resulting WPT coefficients provide one with arbitrary time-frequency resolution of a signal. With the aid of statistical-based feature selection criteria, many of the feature components containing little discriminant information could be discarded, resulting in a feature subset having a reduced number of parameters without compromising the classification performance. The extracted reduced dimensional feature vector is then used as input to a neural network classifier. This significantly reduces the long training time that is often associated with the neural network classifier and improves its generalization capability     

Blind separation of speech mixtures via time-frequency masking

Binary time-frequency masks are powerful tools for the separation of sources from a single mixture. Perfect demixing via binary time-frequency masks is possible provided the time-frequency representations of the sources do not overlap: a condition we call W-disjoint orthogonality. We introduce here the concept of approximate W-disjoint orthogonality and present experimental results demonstrating the level of approximate W-disjoint orthogonality of speech in mixtures of various orders. The results demonstrate that there exist ideal binary time-frequency masks that can separate several speech signals from one mixture. While determining these masks blindly from just one mixture is an open problem, we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided. Motivated by the maximum likelihood mixing parameter estimators, we define a power weighted two-dimensional (2-D) histogram constructed from the ratio of the time-frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters. The histogram is used to create time-frequency masks that partition one of the mixtures into the original sources. Experimental results on speech mixtures verify the technique. Example demixing results can be found online at http://alum.mit.edu/www/rickard/bss.html.     

基于Radon-STFT变换的含噪LFM信号子空间分解

由于线性调频信号占有非常宽的频带,用奇异值分解就不能将含噪线性调频信号分解成信号子空间和噪声子空间,针对这一缺陷,本文提出了一种基于时频面旋转的含噪线性调频信号的子空间分解算法。文中分析了算法的性质,并提出了“伪信号子空间”的概念和用于检测直线倾角的Ｒａｄｏｎ－ＳＴＦＴ变换,理论分析和仿真实验的结果表明了这种子空间分解方法对一类含噪线性调频信号是可行的。     

Robust L-estimation based forms of signal transforms and time-frequency representations

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.