Iterative design of DSP cosine windows by placing spectrum zeros,and some new classes of DSP cosine windows

Windows are used in digital signal processing in order to reduce leakage in spectral analysis and to estimate signal parameters in non-coherent sampling. This paper deals with design theory and presents an algorithm that enables the design of cosine windows with spectra fulfilling various prescribed properties (belonging to various window classes) and window order up to 10. The design is based on iterative window spectrum zero placing. The proposed algorithm was implemented in Matlab, but other mathematical tools can also be used. In addition to the design of all three classes of Rife and Vincent windows and of flattop windows, this method also enables the design of windows with different properties, corresponding to five newly-defined window classes. Both symmetrical and periodic (DFT) windows can be designed. The use of windowing for a range of signal parameter estimation is mentioned and referenced, the principle of the window design method is described, and definitions of the new window classes and examples of designed windows are presented. A graphical user interface of the window design described in this paper in VBA-Excel is accessible free of charge on the www site http://measure.feld.cvut.cz/en/DCW.     

Better narrowband spectral measurements

Spectrum analysis based on traditional FFT techniques is a widely available, commonly understood and general purpose tool for use with mechanical systems. In applications such as system identification, modal analysis and rotating machinery signature analysis, relevant information content in signals is greatest near narrowband phenomena in the frequency domain. Effort should be focused on reducing bias error in these regions in preference to reducing variance error. Time aliasing methods of spectrum analysis can result in superior bias error reduction, producing an accurately sampled spectral estimate and permitting window function characteristics to be decoupled from the DFT resolution, or frequency line spacing. Windows created with time aliasing can be optimized by adjusting the amount of time or frequency localization, according to the type of spectrum being measured. Assuming conventional criteria, time aliased windows can achieve better mainlobe and sidelobe characteristics than other windows. An innovative approach, appropriate with continuous spectra, is to use the window as a discrete sampling function in frequency to eliminate bias error inherent in the effective convolution between window and signal transform. Both approaches have been successfully implemented and results are presented using time aliased spectral estimates showing more accurate measurements of narrowband phenomena when used in applications of rotating machinery vibration and system identification.     

相位式激光测距谱分析鉴相的无偏改进

针对相位式激光测距中的鉴相误差,建立了谱分析鉴相的误差模型,提出了在数据预处理中引入希尔伯特变换来消除相位差估计偏差的测量方法.分析了传统谱分析鉴相的偏差和方差,指出这些测量偏差受初相位的影响,在高速测距中不容忽略.提出了一种无偏改进方法,通过窗函数法设计正弦信号的简易希尔伯特变换器,将离散傅里叶变换的对象转换为解析信号,在仅增加4次加减法运算和2次移位操作的情况下,实现了近似无偏谱分析鉴相.仿真分析和实验验证结果表明,鉴相均值与真实相位差相同;当信噪比为40 dB时,每秒百万次高速鉴相的误差为0.1°;当调制频率为100 MHz时,测距精度达到0.4 mm.实验表明,将希尔伯特变换应用于谱分析鉴相,可实现高准确度相位差测量,并可应用于高速相位式激光测距.     

Accuracy analysis of the amplitude estimation of a sine-wave by the energy-based method using the direct and indirect procedures

The energy-based method (EBM) can be used to estimate the amplitude of a sine-wave either directly from Discrete Fourier Transform (DFT) samples or indirectly. In this paper the accuracies achieved with both these approaches are compared when some of the most commonly used cosine class windows are adopted. The effect on the estimation accuracy of the algorithm error, the spectral interference from the image component, and wideband noise superimposed to the sine-wave signal are separately evaluated and compared. The statistical efficiencies of both procedures with respect to the unbiased single-tone Cramér-Rao lower bound are determined and compared. Moreover, the overall root mean square of the amplitude estimation error achieved when taking into account all the three contributions above is derived for both direct and indirect estimation procedures. The accuracy of the obtained expressions is verified by means of computer simulations. Besides, experimental data validate the theoretical results.     

Method of compensation for systematic errors in goniometric systems

A method based on invariants of in-plane motion of an object is developed for compensation of systematic errors of measurements in goniometric systems. Exact equations are derived for systematic errors of measurement of the object latitude with ignored fluctuating errors of measurement. Analytical expressions are also derived to calculate the standard deviation of the error in estimating systematic errors being taken into account, which allow us to impose grounded requirements to tactical and technical characteristics of goniometric systems designed for observation of various objects.     

高速列车会车压力波对侧窗的影响

高速列车会车时产生的空气压力波动会给交会车辆的侧窗造成很大的冲击,有可能出现破窗事故,给乘客和列车运行带来安全隐患。以三维、非稳态、粘性雷诺时均方程和k-ε两方程紊流模型为基础,采用移动网格的有限体积数值计算方法,仿真分析5种车速(200km/h、250km/h、300km/h、350km/h、400km/h)条件下明线和长隧道内等速会车的动态过程。得到侧窗上完整的会车压力波变化曲线。计算结果表明,明线会车与长隧道内会车产生的压力波对列车侧窗的影响有很大的不同,长隧道内会车时在交会车辆侧窗上产生的气动负压波峰值比明线会车时产生的负压波峰值要大将近一倍,因此不能将明线上会车压力波变化结论外推到隧道内会车情况。以计算结果为基础,分析会车引起破窗的原因和评价侧窗强度的方法。在进行高速列车侧窗设计时,不但要考虑窗玻璃本身的抗冲击强度,还必须考虑列车侧窗的安装强度。相同面积的侧窗,周长大的车窗更有利。     

采用最优多分辨率快速S变换的电能质量分析

为兼顾电能质量信号分析的类型识别与参数估计需要,设计一种最优化多分辨率快速S变换(OMFST),用于电能质量信号识别与参数估计。首先,分析不同时-频分辨率下时间-幅值曲线与频率-幅值曲线中,扰动起、止处峭度与扰动参数估计误差间的关系;之后,根据离差最大化法,确定不同频率范围内最优窗宽调整因子,并通过3次样条插值法进行拟合,自适应调整不同扰动信号识别和参数估计所需最优窗宽;然后,针对扰动信号基频与扰动所在的中、高频频域范围进行OMFST处理;最后,从原始信号、原始信号傅里叶谱和OMFST变换结果中提取5条特征,构建基于模糊决策树的扰动分类器,识别13种电能质量信号,并估计电能质量信号参数。仿真实验和实测数据分析表明,新方法能够满足电能质量复合扰动参数估计需要,参数估计误差低于广义S变换等方法,同时保留了良好的分类能力。     

用动态光散射现代谱估计法测量纳米颗粒

为了解决目前动态光散射软件信号分析法采用的自相关和功率谱估计存在分辨率和方差较低,以及能谱泄漏问题,提出了基于现代功率谱估计的动态光散射信号分析法。对该系统所采用的现代功率谱估计算法和测量系统进行了研究。首先,介绍了动态光散射测量法涉及的光子相关光谱理论和散射光谱估计理论。接着,描述了基于现代功率谱估计的动态散射光谱法,特别是其中阶数p的计算方法。然后,介绍了测量系统,包括硬件部分的光学系统和信号采集处理系统,软件部分的系统开发流程。最后,对粒径分别为30、50、100nm的乳胶球标准颗粒溶液(透光率为96%)进行了实验。实验结果表明:现代谱估计分析法的测量均值误差和重复性误差的平均值分别为1.88%和1.62%,满足国标要求的均值误差和重复性误差2%。     

The error analysis of digital measurements of electrical power

Digital methods of electrical power measurements with non-sinusoidal current have become more important owing to the growing application of thyristor control. The estimation of errors by the sampling methods of measurement is complicated on account of the wide and often difficult to define frequency voltage and current spectrum. Two possible methods of error estimation are described in this paper; partly for measurement in an AC circuit with thyristor control, partly for measurement on pulse-controlled induction motors.     

PHASE DIFFERENCE CORRECTION METHOD FOR PHASE AND FREQUENCY IN SPECTRAL ANALYSIS

A new method, phase difference corrections method is developed to correct the frequency and phase of spectrum peak. The continuous time-domain signal is separated into two segments and fast Fourier translation (FFT) is carried out for them, respectively. The frequency and phase are corrected using the phase difference of corresponding discrete spectral lines. Furthermore, the amplitude can also be rectified using the formula of window function spectrum. This method, with good adaptability, high speed and accuracy, is theoretically simple. It can resolve the frequency by means of phase difference directly without the formula of window function. Simulation shows that the single-component frequency, phase and amplitude of theoretical signal can be corrected satisfactorily, with frequency error less than 0.0002 frequency resolution, phase 0.1° and amplitude 0.0002. If the signal involves noise, the mean corrected errors are less than 0.001 frequency resolution, 1° for phase, and 0.01 for amplitude, respectively, and the maximum corrected errors of one segment are less than 0.01 frequency resolution, 1° and 0.03, respectively.     

Measurement of active power by time domain digital signal processing

This paper compares DSP time domain algorithms of one-phase active power measurement by non-coherent sampling that are superior to some frequency domain algorithms in active power estimation of non-sinusoidal signals. The measurement bias, uncertainty and sampling time necessary for the required accuracy are compared for various data windows with the use of simulations and measurements. Both monofrequency and multifrequency signals are dealt with. Analytical formulas are presented for the active power bias for rectangular and general cosine windows and for standard uncertainty of active power measurement. A simple method is described for correction of the multiplexing delay in power measurement using multiplexing DAQ boards. The information from this paper can also be used for measuring energy consumption and three-phase power.     

离散频谱能量重心法频率校正精度分析及改进

研究噪声对离散频谱能量重心法的频率校正精度的影响,推导了在高斯白噪声背景下用能量重心法对加对称窗的离散频谱进行校正的频率误差理论公式,分析找错和找对最大值谱线情况下的理论误差和某些情况下校正误差较大的原因,为了提高能量重心校正法的频率校正精度,提出用谱线间相位差为阈值作为选择用3条或4条谱线进行校正依据的改进措施。通过对加Hanning窗的离散频谱进行计算机仿真计算,结果表明在大噪声背景下改进的能量重心校正法有很高的频率校正精度,与理论推导十分吻合,验证了理论推导的正确性,表明改进后的能量重心法具有更高的抗噪性能,扩大了能量重心校正法的工程应用范围。     

基于泄漏对消的电力谐波相角高精度估计算法

采用快速傅里叶变换(FFT)进行电力系统谐波分析时,受频谱泄漏和栅栏效应的影响,相角估计误差往往较大.为减小这类误差,提出一种基于频谱泄漏对消的谐波相角高精度估计算法,结合余弦组合窗时域和频域特性,综合考虑长、短范围频谱泄漏的影响,推导了基于余弦组合窗的插值FFT谐波相角计算式.该算法首先运用基于余弦组合窗的插值FFT方法获得频率偏差估计值,然后采用离散频谱泄漏对消方法进行信号谐波相角估计,实现简单,准确度高.非同步采样情况下,采用典型余弦组合窗(Hanning、Blackman、Blackman-Harris、Rife-Vincent(I)、Nuttall等)进行信号谐波相角估计的仿真实验与应用验证了本文算法的准确性和有效性.     

Modelling of errors in measurement

The purpose of this paper is to show different standpoints concerning the modelling and calculation of measurement errors, to discover reasons for topical metrological problems in error analysis, to mention selected confidence limits of measurement errors which have been proved and to recommeend future activities to the unified application of proved error models as well as the concentration of investigations on systematic and residual errors which are insufficiently mastered today.     

Bias error due to windows for the Wigner–Ville distribution estimation

The Wigner–Ville distribution has been recognized as a useful method for time-frequency analysis of non-stationary signals. For mechanical signatures such as vibration and acoustic signals it has demonstrated a very good ability to reveal what actually happens, which is not the case if the signals are processed by conventional methods such as spectrum analysis and amplitude-time analysis. Because of these promising figures for the Wigner–Ville interpretation of mechanical signatures, the possible errors associated with estimation, which are mainly due to the finite record length, have not been analysed. In this paper, the error due to the time window which changes with respect to time, and the error associated with the smoothing process have been analysed theoretically. The error produced by employing a time window has been found to be proportional to the frequency of curvature of the Wigner–Ville distribution and that associated with smoothing has turned out to be proportional to even numbers of derivatives with respect to time and frequency.     

Online Detection of Broken Rotor Bar Fault in Induction Motors by Combining Estimation of Signal Parameters via Min-norm Algorithm and Least Square Method

Current research in broken rotor bar (BRB) fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current. Compared with a discrete Fourier transformation, the parametric spectrum estimation technique has a higher frequency accuracy and resolution. However, the existing detection methods based on parametric spectrum estimation cannot realize online detection, owing to the large computational cost. To improve the efficiency of BRB fault detection, a new detection method based on the min-norm algorithm and least square estimation is proposed in this paper. First, the stator current is filtered using a band-pass filter and divided into short overlapped data windows. The min-norm algorithm is then applied to determine the frequencies of the fundamental and fault characteristic components with each overlapped data window. Next, based on the frequency values obtained, a model of the fault current signal is constructed. Subsequently, a linear least squares problem solved through singular value decomposition is designed to estimate the amplitudes and phases of the related components. Finally, the proposed method is applied to a simulated current and an actual motor, the results of which indicate that, not only parametric spectrum estimation technique.     

机电一体化家用擦窗机的设计

为确保高层住户窗户玻璃擦拭人员的安全,经过对当前多种擦拭方式的分析和总结,提出了机电一体化家用擦窗机的设计。在整机方案设计的基础上,分别对机械结构、动力与控制三部分进行了详细的规划与设计,确定了各部分的主要功能和实现方式。样机试验表明,该机电一体化家用擦窗机结构、功能设计合理,工作状况良好,适合于高空家居玻璃的擦拭。     

数据采集系统内部自动校准模型的建立

提出了由数据采集系统内部自动校准以零偏误差和增益误差为主的日常测试误差。依据若干合理的假设,建立了适用于数据采集系统中每次上电后通道自动校准的一系列模型:调零模型、标定模型、测量模型,并得出了如下结论:这三个模型均满足分段线性关系;测试模型的零偏可由调零模型消除;测试模型的增益可由标定模型确定。经实际操作验证,该方法正确、简便。     

基于RBF神经网络的数字闭环光纤陀螺温度误差补偿

为了消除数字闭环光纤陀螺温度误差,设计了基于径向基函数（RBF）神经网络的温度误差补偿方案,对该方案所采用的标度因数误差模型和偏置误差模型进行了研究。首先,根据光纤陀螺的温度误差分布情况设计了标度因数误差和偏置误差联合补偿的方案。接着,将基于多尺度分析的噪声和趋势项分离算法应用于建模数据预处理,以提高建模数据准确性。然后,建立了RBF神经网络模型,并改进模型的学习方法以防止网络的过拟合。最后,讨论了模型输入向量对神经网络规模的影响。温度补偿的结果表明：标度因数误差模型的残差均方（RMS）达到0.73 ,偏置误差模型的RMS达到0.051 。该建模方法可以满足中、高精度光纤陀螺实时温度补偿的要求。     

基于Kaiser窗双谱线插值FFT的谐波分析方法

为进一步减少加窗插值FFT的频谱泄漏和栅栏效应,提出了基于Kaiser窗的双谱线插值FFT的电力谐波分析方法,运用多项式拟合求出了实用的插值修正算式,推导了信号基波与各次谐波频率、幅值、初相角的计算式。仿真结果表明,Kaiser窗函数设计实现灵活、抑制频谱泄漏效果好,基于Kaiser窗的双谱线插值FFT方法能有效克服基波频率波动与白噪声对谐波分析的影响,在非整数周期截断条件下,对含21次谐波信号的频率计算相对误差仅为1.4×10%,幅值计算相对误差≤0.002%,初相位计算相对误差≤0.0001%,三相谐波电能计量应用实践证明了该方法的正确性。