基于前后向子分段和频移补偿的频率与相位联合估计器

频率估计和相位估计是物理学中的两个基本的测量问题。现有的估计器难以对这两个参数实现高精度的联合测量。为实现联合测量,对已有前后向子分段频率估计器做如下两方面改进:(1)对前、后向子分段快速傅里叶变换(Fast Fourier Transform,FFT)谱峰相位值做平均,获得中心样点的瞬时相位估计;(2)引入频移补偿措施,使得前、后向子分段的峰值谱能量更为集中,增强了估计器抵御噪声的能力,同时提升了估计器的频率和相位估计精度。理论分析和仿真实验表明,该联合估计器性能高于原有前后向子分段估计器和全相位FFT/FFT相位差估计器,对于频率偏离情况,其频率估计方差为克拉美-罗限的4/3倍,其相位估计方差可达到克拉美-罗限。     

离散频谱相位差校正方法研究

在综合分析三种离散频谱相位差校正方法特点的基础上,通过仿真研究,得出在无噪声和小噪声情况下,第一种相位差法（连续采两段信号分别作相同点数FFT）优于第二种相位差法（采一段信号分别作N点和前面N／2点FFT）和第三种相位差法（第一段信号,再构造新序列：将原时域序列前N／2点平移N／4点,将序列的前后N／4点置零,分别对原序列和新序列进行FFT分析,利用对应峰值谱线的相位差进行频谱校正的通用方法）。在大噪声情况下,第三种相位差法的正精度高于其它两种方法。对于相隔较近的频率成分（不小于4个频率分辨率）。第一种和第三种相位差法均高于第二种方法,在小噪声的实际工程中,推荐使用第一种相位差法加Hanning窗进行校正,幅值误差小于1％,频率误差小于0．02个频分分辨率,相位误差小于5度。     

基于FFT的一种计及负频率影响的相位差测量新方法

用FFT法测量低频正弦信号相位差时,精度明显下降,甚至无法测量,其主要原因之一是模型中忽略了负频率成分的贡献.基于FFT法,提出了一种计及负频率影响的相位差测量方法,分别给出了加矩形窗和加汉宁窗对应的相位差计算公式.仿真结果表明,在无噪声背景下.具有很高的精度,尤其是加汉宁窗后,误差接近双精度运算的下限;在噪声背景下,该方法的测量精度也高于FFT法.提出的测量方案简单实用,特别适用于频率很低或接近奈奎斯特频率的正弦信号相位差测量.     

频谱泄漏校正的多频实信号频率估计算法

为抑制多频实信号中负频率频谱泄漏和正频率频谱间相互泄漏对频率估计的影响,提出一种频谱泄漏校正的频率估计算法。利用FFT法对采样信号进行预处理,得到每个分量的频谱索引;对信号频谱进行插值分析,构造所有负频率和非待估计正频率的频谱插值;采用相减策略将信号频谱插值和构造的频谱插值相减,得到抑制了频谱泄漏的待估计正频率频谱插值;对生成的频谱插值进行分析,得到各分量频谱偏移量估计值;经迭代计算得到各分量精确的频率、幅值和初相位估计值。在不同频率间隔、不同信噪比等条件下的仿真实验结果表明:所提算法具有良好的频率估计性能,有效抑制了频谱泄漏的影响,提高了多频实信号的频率估计精度,使得频率估计值的均方误差更接近于克拉美罗下限。此外,在LFMCW雷达实验平台上进行了测距实验,检验了所提算法的实际应用效果。     

相减策略的含噪多频实信号频率估计算法EI北大核心CSCD

为抑制频谱泄漏对多频实信号频率估计的影响,提出一种新的频率估计算法。利用FFT法和相减策略对采样信号进行处理,逐步得到各分量的频谱最大值索引,以及各分量频谱偏移量和复幅值粗略值;构造包含所有非待估计频率分量的参考信号,利用相减策略从采样信号中减去参考信号,得到待估计的单频复信号,并对其频谱进行两点插值计算,得到该分量较精确的频谱偏移量和复幅值;然后,通过相减策略和频谱分析,逐步得到所有分量较精确的频谱偏移量和复幅值;通过迭代计算得到各分量精确的频率估计值。同时,可得到各分量精确的幅值和初相位。在无噪声、不同频率间隔等条件下进行了频率仿真试验。结果表明:所提算法有效抑制了频谱泄漏的影响,提高了多频实信号的频率估计精度,频率估计值的均方误差比其他优秀算法更靠近克拉美罗下限。     

计及负频率的DFT与DTFT相位差测量误差分析

针对噪声背景下计及负频率的DFT(Discrete Fourier Transform)与DTFT(Discrete Time Fourier Transform)相位差测量误差问题,用误差理论分别推导出高斯白噪声背景下计及负频率的DFT与DTFT相位差估计方差计算公式。对不同的泄漏误差系数、采样序列长度及信噪比,在负频率影响条件下进行计算验证。结果表明,仿真结果与计算结果一致,表明相位差测量误差分析公式的正确性。提升频率估计精度、增加采样序列长度、提高信号信噪比,可有效提升计及负频率的DFT与DTFT相位差测量方法精度。采样序列长度大于2048点或信噪比大于5 d B时,相位差测量精度提升有限,且DTFT相位差测量方法对频率估计精度更敏感。     

振动信号的幅值和相位计算方法分析

给出了基于Kaiser窗FFT频谱法、正弦逼近法和全相位时移相位差法计算振动信号幅值和相位的计算方法,并使用三种方法分别对单一的正弦信号以及混有噪声和其它频率的正弦信号进行了测试。通过测试数据对三种方法的信号处理效果进行了分析比较,阐述了不同计算方法的优缺点。比较结果显示具有抑制频谱泄漏和"相位不变性"的全相位谱分析结合高精度相位差法而得的全相位时移相位差法精度更高,应用范围更广。     

信号相位差的算法研究

研究求信号相位差的三种算法。首先利用相关分析,对于同频信号,互相关函数保留频率信息和相位差信息;另外可以采用LMS算法设计自适应相位差估计器,具有较高的精度;还可以借助基于快速谱分析(FFT)技术的快速谱分析测相模块,实现信号的相位差计算。     

基于DTFT的一种低频振动信号相位差测量新方法

现有基于DFT频谱分析的相位差测量方法在测量低频振动信号的相位差时，精度明显下降，甚至无法测量，其主要原因之一是忽略了频谱中的负频率成分贡献。基于离散时问傅里叶变换（DTFT），提出了一种计及负频率影响的低频振动信号相位差测量方法，分别给出了加矩形窗和加汉宁窗对应的相位差计算公式。仿真及实测结果表明，在无噪声背景下，该方法具有很高的精度，误差接近双精度运算的下限；在噪声背景下，其测量精度仍高于传统的DFT频谱分析方法。提出的测量方案简单实用，特别适用于频率很低或接近奈奎斯特频率的振动信号的相位差测量。     

基于相位差校正法的全息谱研究

针对传统全息谱在噪声干扰下精度降低的问题,提出了一种新的基于相位差校正法的全息谱分析方法。该方法首先对时域信号加窗截断后进行FFT变换,然后引入相位差法校正其频率、幅值和相位,最后合成全息谱图。通过仿真及对柔性转子实验台的振动信号的分析,表明基于相位差校正法的全息谱可以明显提高其分析精度,更加精确而有效地诊断旋转机械的故障。     

A new wideband spread target maximum likelihood estimator for blood velocity estimation. I. Theory

The derivation and theoretical evaluation of new wideband maximum-likelihood strategies for the estimation of blood velocity using acoustic signals are presented. A model for the received signal from blood scatterers, using a train of short wideband pulses, is described. Evaluation of the autocorrelation of the signal based on this model shows that the magnitude, periodicity, and phase of the autocorrelation are affected by the mean scatterer velocity and the presence of a velocity spread target. New velocity estimators are then derived that exploit the effect of the scatterer velocity on both the signal delay and the shift in frequency. The wideband range spread estimator is derived using a statistical model of the target. Based on the point target assumption, a simpler wideband maximum-likelihood estimator is also obtained. These new estimation strategies are analyzed for their local and global performance. Evaluation of the Cramer-Rao bound shows that the bound on the estimator variance is reduced using these estimators, in comparison with narrowband strategies. In order to study global accuracy, the expected estimator output is evaluated, and it is determined that the width of the mainlobe is reduced. In addition, it is shown that the height of subsidiary velocity peaks is reduced through the use of these new estimators.     

FFT幅相联合的快速高精度频率估计方法

快速傅里叶变换（Fast Fourier Transform,FFT）常用于信号频率估计,采用填零的方法可降低幅度谱频率搜索间隔的量化误差,但是会使频率估计的计算量成倍增加。本文提出了一种FFT幅相联合的快速高精度频率估计算法,首先利用信号采样的频谱序列和尾首样本差确定幅度谱及峰值位置,然后由频谱序列在幅度谱峰值位置和信号采样的尾首样本差来确定频率搜索间隔的量化误差校正值。因此,所提方法同时利用了幅度谱峰值的位置信息与相位信息。分析结果表明,与仅基于幅度谱搜索的FFT算法相比,所提方法的计算复杂度更低,且定位精度更高。     

A new adaptive mean frequency estimator: application to constant variance color flow mapping

A class of adapted mean frequency estimators is proposed for color flow mapping. These estimators can be fitted to the specific characteristics of a given Doppler signal to optimize the compromise between the range of analysable frequencies and the variance of mean frequency estimation. A sub-optimal estimator is derived for real-time applications, and an adaptive criterion based on the Doppler signal variance is developed for color flow mapping applications. Its performance is compared to that of the usual correlation phase estimator on simulated Doppler signals and on synthetic Doppler images. An improvement in image quality is achieved, mainly for low signal-to-noise ratio Doppler signals.     

Estimation of mean frequency and variance of ultrasonic Doppler signal by using second-order autoregressive model

In order to estimate the mean frequency and variance of the diagnostic ultrasound Doppler signal in the presence of clutter noise, a new estimator using a second-order autoregressive (AR) model, called the AR estimator, is proposed. The sampled signal that contains information of both the Doppler signal and clutter is described by the second-order AR model with two poles. The mean frequency and variance of a unidirectional Doppler signal can be estimated, respectively, from the phase and the magnitude of the pole, with larger phase between the two poles. If the clutter is not completely rejected, all conventional estimators, including the autocorrelation (AC) estimator, result in erroneous estimations for the mean frequency and variance of the Doppler signal, whereas the AR estimator gives an accurate estimation. In the absence of clutter, however, the performance of both the AC and AR estimators are similar. If the blood flows in both directions in a sample volume and the clutter is rejected to the extent that it no longer obscures the Doppler signal, the proposed method can estimate simultaneously the mean frequencies and variances of both the forward and reverse blood flows. The performance of the proposed AR estimator was compared with that of the AC estimator by computer simulations and experiments, and it was found that when the number of available sampled data is small, the AR estimator does not require the use of a clutter filter, which simplifies Doppler signal detection.     

Phase II Monitoring of Nonlinear Profile Variance Using Wavelet

In some statistical process control applications, the quality of a process or a product can be characterized by a nonlinear relationship between a response variable and one or more explanatory variables. Monitoring nonlinear profiles using nonlinear regression has been proposed by several researchers as a potential area for research. To avoid disadvantages of parameter estimation in nonlinear regression, we used nonparametric regression with wavelets for monitoring nonlinear profiles. In nonparametric regression framework, traditional variance estimator is not proper; other estimators should be used instead. Parametric or nonparametric control charts in phase II are proposed to monitor error term variance when nonparametric regression with wavelet is used. Multivariate control chart based on regression coefficients (approximate wavelet coefficients) is added to variance control chart to check stability in the process mean. It is well known that the performance of control schemes in detecting shifts in multivariate control charts deteriorates as the dimension of regression coefficient increases. To improve the performance of control schemes, we considered decomposition level as a smoothing parameter, which determines the form of regression function (size of approximate wavelet coefficients vector) in nonparametric regression with wavelet. A method based on an analysis of variance is proposed to determine the optimal decomposition level. The statistical performances of the proposed methods are evaluated using average run length criterion using vertical density profile data. Numerical results indicate that the proposed methods perform satisfactorily. Copyright © 2012 John Wiley & Sons, Ltd.     

频谱分析中用于相位和频率校正的相位差校正法

提出了一种对连续时域信号分前后两段作傅里叶变换,利用其对应离散谱线的相位差校正出谱峰处的准确频率和相位的新校正方法——相位差校正法,通过窗谱函数的公式还可以校正其幅值,以解决离散频谱分析中由于谱峰谱线没有对正峰顶时所带来的较大误差。该方法原理简单,通用性好,运算速度快,校正精度高,可以在不知道窗谱函数表达式的情况下,直接用其相位差进行求解。仿真研究表明,对单频率成分的频率、相位、幅值进行校正,频率误差小于0.0002个频率分辨率,相位误差小于0.1 度,幅值误差小于0.02% 。     

离散频谱四点能量重心校正法及抗噪性能分析

在对比离散频谱能量重心法采用不同点数时的频率、幅值和相位校正精度的基础上提出了4点能量重心校正法,推导了高斯白噪声背景下单频率谐波信号采用4点能量重心法进行频率、幅值和相位校正的统计方差公式,通过仿真计算验证了其正确性.分析对比了采用不同点数进行能量重心校正时的优缺点,建议在工程中采用Han-ning窗4点能量重心法进行谐波信号离散频谱校正.     

A study on nonlinear averagings to perform the characterization ofpower spectral density estimation algorithms

This paper analyzes algorithms which are suitable for spectral estimates of noisy signals in the frequency domain based on the use of the fast Fourier transform (FFT). Several causes of inaccuracy are analyzed and characterized so that the expressions of different components of error on the power spectral density (psd) estimate are given, in terms both of spectral properties of noise and typical parameters of the used filter. These simple expressions point out how an appropriate choice of some window parameters may increase considerably the accuracy of the estimate. The effects of choice on the accuracy are examined. In any case, the performance of the psd estimator can be improved by adopting linear or nonlinear averaging techniques; in the paper the statistical properties of geometric mean of periodograms are particularly examined and compared with those of the more traditional Welch's method. It is proved that, under appropriate conditions, the geometric mean produces a reduction both of bias and variance of psd. Numerical simulations confirm these theoretical results     

离散频谱分析比值校正法幅值和相位的抗噪性分析

谐波信号离散频谱分析的比值校正法(内插法)在无噪声时是一种准确的校正方法,只存在计算时的舍入误差,但在包含噪声尤其信噪比较低时,校正精度会有所下降,甚至误差很大.研究了比值校正法的幅值与相位加不同的窗函数及加性高斯白噪声时的统计方差公式,并通过不同信噪比下的仿真验证了其准确性.建议避免在归一化频率误差较低的情况下使用加矩形窗的比值校正法来校正相位.     

High Accuracy Network Cardinalities Estimation by Step Sampling Revision on GPU

Host cardinality estimation is an important research field in network management and network security. The host cardinality estimation algorithm based on the linear estimator array is a common method. Existing algorithms do not take memory footprint into account when selecting the number of estimators used by each host. This paper analyzes the relationship between memory occupancy and estimation accuracy and compares the effects of different parameters on algorithm accuracy. The cardinality estimating algorithm is a kind of random algorithm, and there is a deviation between the estimated results and the actual cardinalities. The deviation is affected by some systematical factors, such as the random parameters inherent in linear estimator and the random functions used to map a host to different linear estimators. These random factors cannot be reduced by merging multiple estimators, and existing algorithms cannot remove the deviation caused by such factors. In this paper, we regard the estimation deviation as a random variable and proposed a sampling method, recorded as the linear estimator array step sampling algorithm (L2S), to reduce the influence of the random deviation. L2S improves the accuracy of the estimated cardinalities by evaluating and remove the expected value of random deviation. The cardinality estimation algorithm based on the estimator array is a computationally intensive algorithm, which takes a lot of time when processing high-speed network data in a serial environment. To solve this problem, a method is proposed to port the cardinality estimating algorithm based on the estimator array to the Graphics Processing Unit (GPU). Experiments on real-world highspeed network traffic show that L2S can reduce the absolute bias by more than 22% on average, and the extra time is less than 61 milliseconds on average.