Signal enhancement by time-frequency peak filtering

Time-frequency peak filtering (TFPF) allows the reconstruction of signals from observations corrupted by additive noise by encoding the noisy signal as the instantaneous frequency (IF) of a frequency modulated (FM) analytic signal. IF estimation is then performed on the analytic signal using the peak of a time-frequency distribution (TFD) to recover the filtered signal. This method is biased when the peak of the Wigner-Ville distribution (WVD) is used to estimate the encoded signal's instantaneous frequency. We characterize a class of signals for which the method implemented using the pseudo WVD is approximately unbiased. This class contains deterministic bandlimited nonstationary multicomponent signals in additive white Gaussian noise (WGN). We then derive the pseudo WVD window length that gives a reduced bias when TFPF is used for signals from this class. Testing of the method on both synthetic and real life newborn electroencephalogram (EEG) signals shows clean recovery of the signals in noise level down to a signal-to-noise ratio (SNR) of -9 dB.     

一种低副瓣无混叠的线性调频信号时频分析方法

作为通信与勘探中广泛使用的一类信号,线性调频信号的参数分析经常采用基于Wigner-Ville分布(WVD)的时频分析方法。该方法具有高时频分辨率,但在交叉项、高副瓣以及频谱混叠问题上存在缺陷。该文提出一种名为空间变迹重排Wigner-Ville分布(SVA-rWVD)的时频分析方法,结合空间变迹技术(SVA)的副瓣抑制能力及短时傅里叶变换(STFT)的无混叠无交叉项特性,得到一个新的时频分布。基于单分量和多分量线性调频信号的仿真实验结果表明,该方法得到的时频分布可以降低副瓣水平至–40 dB以下同时消除交叉项及频谱混叠现象。     

一种基于多窗宽度STFT的PSWFs信号时频分析方法

固定窗宽度的短时傅里叶变换(Short Time Fourier Transform,STFT)时频分辨率是固定的,难以对频率时变的椭圆球面波函数(Prolate Spheroidal Wave Functions,PSWFs)信号的时频分布特性进行全面分析.剖析了窗宽度对不同参数PSWFs信号STFT时频分布的影响,...     

雷达动目标变换域相参积累检测及性能分析

从雷达动目标信号变换实现相参积累的角度出发,选取4种典型的相参积累方法：短时傅里叶变换(STFT)、维格纳-威利分布(WVD)、平滑伪维格纳-威利分布(SPWVD)及分数阶傅里叶变换(FRFT),并将其应用于雷达动目标检测。重点研究了采样频率、脉冲数、输入信噪比(SNR)对相参积累性能以及动目标检测性能的影响。结果表明,FRFT运算速度相对较慢但适用范围最广,尤其在处理噪声背景较强的信号时,能够有效抑制噪声,且参数估计精确度较高,具有良好的时频聚集性,为雷达相参积累检测的工程化应用提供理论支撑。     

抑制维格纳分布交叉项干扰的自谱窗方法

维格纳分布是一种重要的时—频分析方法,但交叉项干扰问题影响了它的推广应用。本文分析了积分核函数的自维格纳分布项和交叉项的正交性质,从而提出一种用真实的自维格纳分布项的函数作为模板与积分核函数作互相关,抑制交叉项的方法。文中建议采用信号的STFT谱作为窗,在时一频平面上处理维格纳分布来实现上述方法,因此,该方法又称为自谱窗法。本文以仿真信号为例,检验了这种方法的效果。     

基于改进时频分析方法的雷达信号瞬时频率估计

瞬时频率估计(Instantaneous Frequency, IF)在雷达信号处理中有着重要的研究意义,时频分布峰值检测是IF估计研究和应用中较为普遍和有效的方法,但由于噪声的影响,时频分布峰值往往偏离真实的IF曲线。针对低信噪比下的IF估计,文中首先对WVD及CWD的时频分布矩阵作Hadamard积,得到一种混合的时频分析方法,而后采用多样本信号时频能量累乘的方法,进一步抑制噪声在时频面上的分布;然后以时频分布峰值在信号自项时频聚集区域的分布概率为准则,计算出时频分布的数据窗长,并根据该窗长得到IF的初始估计;最后依据初始IF,采用交叉置信区间算法对时频分布峰值进行检测,得到信号的瞬时频率估计值。文中对NLFM、LFM和FSK信号的IF估计进行了研究,并与WVD峰值检测法和时频分布一阶矩法进行了比较,仿真结果表明了本文方法的有效性。      

Local polynomial modeling of time-varying autoregressive models with application to time-frequency analysis of event-related EEG

This paper proposes a new local polynomial modeling (LPM) method for identification of time-varying autoregressive (TVAR) models and applies it to time-frequency analysis (TFA) of event-related electroencephalogram (ER-EEG). The LPM method models the TVAR coefficients locally by polynomials and estimates the polynomial coefficients using weighted least-squares with a window having a certain bandwidth. A data-driven variable bandwidth selection method is developed to determine the optimal bandwidth that minimizes the mean squared error. The resultant time-varying power spectral density estimation of the signal is capable of achieving both high time resolution and high frequency resolution in the time-frequency domain, making it a powerful TFA technique for nonstationary biomedical signals like ER-EEG. Experimental results on synthesized signals and real EEG data show that the LPM method can achieve a more accurate and complete time-frequency representation of the signal.     

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.     

A spectral matching approach for parameter and spectral estimationof nonstationary rational processes

The parameter and spectral estimation problems of nonstationary signals are considered. The nonstationary signals are modeled as rational processes with time-varying parameters. The spectral matching approach, which was introduced by Friedlander and Porat (1984), is generalized to the nonstationary case and two new estimators, namely, the time-varying spectral matching estimator (TVSME) and the time-frequency spectral matching estimator (TFSME) are proposed. The proposed methods estimate the parameters of the time-varying rational model by fitting the parametric spectrum expression to an estimated time-frequency distribution of the signal. An approximate statistical analysis is given for both methods along with computer simulation results, illustrating the performance of the proposed estimators     

基于局部多项式傅里叶变换的语音盲源分离

频域的语音信号盲源分离多采用短时傅里叶变换以及Wigner-Ville分布(WVD)求信号的功率谱,而短时傅里叶变换对于多分量信号的频率分辨率受窗函数影响很大,WVD是一种非线性时频变换,处理多分量信号受交叉项影响很大。局部多项式傅里叶变换(LPFT)不仅提高了频率估计精度而且大大减少了时频分布中交叉项的影响。将语音信号表示为多分量的多项式相位信号,对语音信号作二阶LPFT,求得其局部多项式傅里叶变换谱(LPP),并构造时频矩阵,采用联合近似对角化算法求得能使信号功率谱矩阵近似对角化的一个酉矩阵,通过信号的白化以及酉矩阵来估计源信号,有效地分离出了原始信号。仿真结果表明,在噪声环境下可以将两个不同的语音信号进行分离。     

基于时频分析的伪码与线性调频复合体制侦察信号参数估计研究

研究了伪码-线性调频复合体制侦察信号识别的时频分析方法,推导了PRBC-LFM侦察信号的Wigner时频分布函数,通过对＝0 +Kt截面上WVD分析,从中提取了与载频、调频斜率和伪码参数(子脉冲宽度、编码位数、脉冲周期等)有关的特性,设计了参数估计方法,最后在高斯噪声环境下对分析的结果进行了仿真。结果表明该文提出的方法对PRBC-LFM信号的识别优于谱相关方法,而且应用不受调频带宽与伪码谱宽关系的限制。     

形态学滤波与组合时频分布跳频信号参数估计

针对跳频信号参数估计中平滑类维格纳分布（WVD）运算量大和时频分辨率下降等问题,提出一种基于形态学滤波与组合时频分布的跳频参数盲估计方法。该方法首先利用短时傅里叶变换（STFT）和维格纳分布得到跳频信号的组合时频分布,然后通过形态学滤波得到清晰的时频图,进而估计出跳周期、跳变时刻和跳频频率等参数。理论分析和仿真结果表明,与直接利用平滑伪维格纳（SPWVD）进行跳频参数估计相比,该方法计算量更小,估计精确度更高。     

A high-resolution quadratic time-frequency distribution formulticomponent signals analysis

The paper introduces a new kernel for the design of a high resolution time-frequency distribution (TFD). We show that this distribution can solve problems that the Wigner-Ville distribution (WVD) or the spectrogram cannot. In particular, the proposed distribution can resolve two close signals in the time-frequency domain that the two other distributions cannot. Moreover, we show that the proposed distribution is more accurate than the WVD and the spectrogram in the estimation of the instantaneous frequency of a stepped FM signal embedded in additive Gaussian noise. Synthetic and real data collected from real-world applications are shown to validate the proposed distribution     

Adaptive phase extraction: incorporating the Gabor transform in the matching pursuit algorithm

Short-time Fourier transform (STFT), Gabor transform (GT), wavelet transform (WT), and the Wigner-Ville distribution (WVD) are just some examples of time-frequency analysis methods which are frequently applied in biomedical signal analysis. However, all of these methods have their individual drawbacks. The STFT, GT, and WT have a time-frequency resolution that is determined by algorithm parameters and the WVD is contaminated by cross terms. In 1993, Mallat and Zhang introduced the matching pursuit (MP) algorithm that decomposes a signal into a sum of atoms and uses a cross-term free pseudo-WVD to generate a data-adaptive power distribution in the time-frequency space. Thus, it solved some of the problems of the GT and WT but lacks phase information that is crucial e.g., for synchronization analysis. We introduce a new time-frequency analysis method that combines the MP with a pseudo-GT. Therefore, the signal is decomposed into a set of Gabor atoms. Afterward, each atom is analyzed with a Gabor analysis, where the time-domain gaussian window of the analysis matches that of the specific atom envelope. A superposition of the single time-frequency planes gives the final result. This is the first time that a complete analysis of the complex time-frequency plane can be performed in a fully data-adaptive and frequency-selective manner. We demonstrate the capabilities of our approach on a simulation and on real-life magnetoencephalogram data.     

稳定分布噪声下基于Merid滤波的跳频信号参数估计

常规时频分析方法是处理跳频(FH)信号的有力工具,但在稳定分布噪声环境下无法有效地实现参数估计。该文提出基于Merid滤波的时频分析方法对跳频信号进行参数估计。Merid滤波器可以有效地抑制稳定分布噪声,该文先对观测信号进行Merid滤波,再采用短时傅里叶变换(STFT)进行参数估计。仿真结果表明,在稳定分布噪声环境中,该方法的跳频信号参数估计性能优于基于分数低阶和基于Myriad滤波的两种时频分析方法。     

一种基于短时傅里叶变换的机载SAR自聚焦算法

短时傅里叶变换(Short-Time Fourier Transform, STFT)是研究非平稳信号最为广泛使用的重要方法。该文在讨论了利用STFT对线性调频信号(LFM)进行滤波以及调频率估计后,提出一种基于STFT的机载SAR自聚焦算法。该算法首先利用STFT对影响SAR图像质量的主要相位误差二次相位误差(QPE)进行估计和补偿,然后在残余相位误差估计时利用STFT对时变信号进行滤波以提高信杂比(SCR)。仿真和实测数据的处理结果验证了该文算法的有效性。     

基于子带分解WVD的雷达信号时频分析方法

研究利用谐波小波子带分解消除 Wigner-Ville 分布交叉项的雷达信号时频联合分析方法。通过对多分量信号进行子带分解预处理来消除信号之间以及信号与噪声之间的相互影响， 并求取个独立分量的 WVD，最后进行线性求和获得原始信号时频分布。仿真分析结果表明，对于在频域无交叉点的多分量信号，该方法能够有效抑制交叉项和噪声的干扰，提高了时频分辨效果并能准确提取出目标的特征信息，检测效果优于传统 WVD 分析方法，将有助于提高雷达信号检测、特征提取的能力。     

Analysis of Multi-Component Non-Stationary Signals Using Fourier-Bessel Series and Wigner-Hough Transform

We presented a novel Fourier-Bessel (FB) series and Wigner-Hough transform (WHT) method for the analysis of multi-component non-stationary signals. The FB series decomposed multi-component non-stationary signals into mono-component signals. The Wigner-Ville distribution (WVD) was applied to each mono-component signal to analyze its time-frequency distribution (TFD). Summing up the WVDs of the individual components resulted in TFDs of the multi-component signals, where the cross terms and noise were significantly reduced. The Hough transform (HT) was applied on the TFD of the multi-component signal (obtained from FB-WVD). The HT provides an important tool for mapping the signals onto a parameter space where the detection and estimation problems are made easier. This mapping can be used in the detection and parameter estimation of signals which are unknown and embedded in noise.     

Spatial polarimetric time-frequency distributions for direction-of-arrival estimations

Time-frequency distributions (TFDs) are traditionally applied to a single antenna receiver with a single polarization. Recently, spatial time-frequency distributions (STFDs) have been developed for receivers with multiple single-polarized antennas and successfully applied for direction-of-arrival (DOA) estimation of nonstationary signals. In this paper, we consider dual-polarized antenna arrays and extend the STFD to utilize the source polarization properties. The spatial polarimetric time-frequency distributions (SPTFDs) are introduced as a platform for processing polarized nonstationary signals, which are received by an array of dual-polarized double-feed antennas. This paper deals with narrow-band far-field point sources that lie in the plane of the receiver array. The source signals are decomposed into two orthogonal polarization components, such as vertical and horizontal. The ability to incorporate signal polarization empowers the STFDs with an additional degree of freedom, leading to improved signal and noise subspace estimates for direction finding. The polarimetric time-frequency MUSIC (PTF-MUSIC) method for DOA estimation based on the SPTFD platform is developed and shown to outperform the time-frequency, polarimetric, and conventional MUSIC techniques, when applied separately.     

Robust Wigner distribution with application to the instantaneousfrequency estimation

The Wigner distribution (WD) produces highly concentrated time-frequency (TF) representation of nonstationary signals. It may be used as an efficient signal analysis tool, including the cases of frequency modulated signals corrupted with the Gaussian noise. In some applications, a significant amount of impulse noise is present. Then, the WD fails to produce satisfactory results. The robust periodogram has been introduced for spectral estimation of this kind of noisy signals. It can produce good concentration for pure harmonic signals. However, it is not so efficient in the cases of signals with rapidly varying frequency. This is the motivation for introducing the robust WD. It is a reliable TF representation tool for wide class of nonstationary signals corrupted with impulse noise. This distribution produces good accuracy of the instantaneous frequency (IF) estimation. Using the Huber (1981) loss function, a generalization of the WD is presented. It includes both the standard and the robust WD as special cases. This distribution can be used for TF analysis of signals corrupted with a mixture of impulse and Gaussian noise. The presented theory is illustrated on examples, including applications on the IF estimation and time-varying filtering of signals corrupted with a mixture of the Gaussian and impulse noise. The case study analysis of the IF estimators' accuracy, based on the standard and the robust WD forms, is performed. In order to improve the IF estimation, a median filter is applied on the obtained IF estimate