闪烁噪声的自动关函数及其表征

闪烁噪声是一种非平衡随机过程，其功率谱密度函数在频率低端（f=0)发散，无法直接利用Wiener-Khintchine关系得到它的自相关函数，本文采用“降价－积分”方法，得到了频率源中闪烁调频噪声的自相关函数的解析表达式，根据这一结果，分析了频率稳定度的表征原理，指出了频率稳定度表征的实质是将非平稳过程转化为平衡过程并求取时间平均，最后，通过时域分析得到了闪烁噪声的Allan方差表达式。     

弹性—粘弹性复合结构的随机响应分析

本文建立在随机振动时域复模态分析的基础上,利用扩阶状态变量,将弹性－粘弹性复合结构系统的微分积分动力学方程变换成常规的状态方程,提出了一种分析弹性－粘弹性复合结构系统随机响应的方法,得到了弹性－粘弹性复合结构系统在平稳随机激励下响应相关函数矩阵的表达式,并对典型的平稳随机激励（平稳白噪声激励及平稳滤过白噪声激励）情形,进行了分析,得到了典型平稳随机激励下,弹性－粘弹性复合结构系统响应相关函数矩阵的代数解析表达式。所提分析方法简便、易用,无论单自由度系统或多自由系统均可适用。本文方法为粘弹性系统的随机响应分析提供了一条途径。     

弹性-粘弹性复合结构系统的随机响应分析

本文建立在随机振动时域复模态分析的基础上,利用扩阶状态变量,将弹性－粘弹性复合结构系统的微分积分动力学方程变换成常规的状态方程,提出了一种分析弹性－粘弹性复合结构系统随机响应的方法,得到了弹性－粘弹性复合结构系统在平稳随机激励下响应相关函数矩阵的表达式,并对典型的平稳随机激励（平稳白噪声激励及平稳滤过白噪声激励）情形,进行了分析,得到了典型平稳随机激励下,弹性－粘弹性复合结构系统响应相关函数矩阵的复代数解析表达式。所提分析方法简便、易用,无论单自由度系统或多自由度系统均可适用。本文方法为粘弹性系统的随机响应分析提供了一条途径。     

随机参数诱导交流积分器中的随机共振研究

研究了具有随机参数的交流积分器中的随机共振现象。基于线性系统理论,得到了系统输出信噪比的表达式。研究发现,输出信噪比是噪声强度、噪声相关率以及系统参数的非单调函数。信噪比随着激励信号频率的增大而增大,随着信号直流分量的增大而减小。     

《二值噪声作用下线性系统的随机共振》

研究了二值噪声用下的二阶过阻尼线性系统的随机共振现象。基于线性系统理论和相关删去法方法,得到了系统平均输出幅度增益的精确表达式。研究表明：输出幅度增益是噪声的强度和相关时间、系统阻尼系数,以及激励信号的频率的非单调函数;另外,适当的噪声参数和系统参数可以使噪声情况下的输出幅度增益大于无噪声时的输出幅度增益。     

由相位噪声间接测量阿伦方差的研究

振荡器的频率稳定度在时域一般用阿伦方差表征,在频域一般用相位噪声谱密度函数表征,两者存在一定的数学转换关系,即可以由频域测量的相位噪声谱密度函数转换为时域的阿伦方差.t<0.1 ms时短期频率稳定度的时域测量非常困难.利用两者之间的转换关系对振荡器的时域稳定度进行了间接测量,并用实测数据进行了验证.     

埋地管道的非平稳随机振动

将实际地震地面运动看作为非平稳随机过程，研究了埋地管道的非平稳随机响应，考虑地面运动的相关性，导出了轴向和横向振动响应(应力和位移)的相关函数的解析表达式，实例计算了一条埋地管道非平稳随机振动的应力和位移的时间历程。     

相关偏置信号调制噪声和加性噪声驱动线性系统随机共振

研究了偏置信号调制噪声和加性噪声驱动线性系统的随机共振现象。根据线性系统理论,得到了系统输出信噪比的精确表达式。研究结果表明：系统输出信噪比是系统衰减常数、调制信号偏置参数、信号调制噪声强度和加性噪声强度的非单调函数。同时,系统输出信噪比随两种噪声的相关强度成非单调关系。     

一种原子钟频率稳定度的估计方法

为了更合理地评估处于相同实验条件下原子钟的绝对频率稳定度,以理论视角分析了算法模型及求解过程,研究了噪声相关条件下绝对频率稳定度的估计方法。用3台原子钟仿真数据对该方法进行了评定,假设噪声独立条件下随着噪声相关性的增强测试结果不断偏离频率稳定度真值;考虑噪声相关条件下测试结果与频率稳定度真值相对误差不超过1.7%。该方法被进一步应用到中国计量科学研究院实验室4台铯原子钟,360天实际测量数据验证了其有效性。     

循环自相关函数及其切片的解调原理分析

在具有齿轮、滚动轴承等设备的机械故障诊断中,幅值解调分析是非常有用的工具.分析了的基于循环平稳信号的循环自相关函数的解调原理,提出了一种新的解调方法--循环自相关函数切片法,由于平稳信号没有循环平稳的特点,使得该方法对加性平稳噪声具有自动降噪功能.     

Characterization of Frequency Stability: Uncertainty due to the Finite Number of Measurements

We consider the characterization of the frequency stability of signal generators by means of the Allan variance of their fractional frequency fluctuations. As the number m of measurements is always finite, one can only get an estimate of this variance, which is a random function of m. We calculate the variance of the Allan variance for commonly encountered spectral densities of frequency fluctuations and deduce the relative uncertainty in the evaluation of frequency stability, as a function of m. The theory is experimentally checked for white noise of phase and flicker noise of frequency. The main hypothesis of the calculations, i.e., the Gaussian character of frequency fluctuations is verified. The m dependence of the uncertainty (one sigma) in the evaluation of frequency stability agrees with the predicted value.     

Degrees of freedom of the estimate of the two-sample variance inthe continuous sampling method

The two-sample variance, the frequency stability measure in the time domain, is defined in terms of the infinite time average. The estimate of the variance obtained from a finite data set must be accompanied by a confidence interval. Theoretical equations are derived for the variance or degrees of freedom in the chi-square distribution for the continuous sampling method to make more efficient use of a finite set of sampled time data. The results are plotted for degrees of freedom and show that there is considerable improvement in the phase modulation (PM) noise compared with the results for τ-overlap sampling, because of an increased number of τ-averaged frequency samples to be obtained from the time data. For white, flicker, and random-walk frequency modulation (FM) noise the improvements converge to about 100, 30, and 4%, respectively. The reasonableness of the assumption of stationarity of the random process is discussed     

Characterization of Frequency Stability: Uncertainty Due to the Autocorrelation of the Frequency Fluctuations

We considered the general sampling form for the estimate of the Allan variance which is the proposed measure of frequency stability in the time domain, and we defined a variable proportional to the difference between the average fractional frequency fluctuations over the time interval ? to derive the autocorrelation coefficient of the process to which the variable belongs. Calculations of the variance of the estimated Allan variance proved that it may be convergent to its true value with infinite sample number for considered spectral densities of frequency noise. We also applied the results to estimations of frequency measurements to know the influence of the autocorrelation of the process considered. In order to obtain some direct estimates of the confidence of the estimate, distributions of the estimate were plotted by means of computer simulations, and were compared with the chi-square distribution. Those results suggested that for white-and flicker-phase noises (and white-frequency noise) we have to take into account the autocorrelation of the process, while for flicker-or random-walk-frequency noise we may regard the process as a nearly independent (and Gaussian) one.     

Modeling resonator frequency fluctuations induced by adsorbing and desorbing surface molecules

Resonator frequency fluctuations due to adsorption and desorption of molecules on plate electrodes are studied using the principle of mass-loading effects of adsorbed molecules. The study is based on a 525 MHz, AT-cut quartz resonator enclosed in a small crystal holder. Equations relating the surface adsorption rates of the crystal holder to pressure were derived and found to be quadratic polynomial functions of the adsorption rates. Calculations based on these equations show that a contaminant gas with a higher desorption energy creates larger changes in pressure when the temperature is varied. The function describing the frequency fluctuations due to any one contaminant site is a continuous-time Markov chain. Kolmogorov equations and an autocorrelation function for the Markov chain are derived. The autocorrelation and spectral density function of resonator frequency fluctuations are derived. The spectral density of frequency fluctuations at 1 Hz is studied as a function of pressure, temperature, and desorption energy of molecules. The noise levels for a contaminant gas with one type of molecules are found to be lower for lower desorption energies, and higher at lower pressures.     

Noise autocorrelation in magnetic recording systems

This paper describes a new technique for measuring the noise autocorrelation in magnetic recording systems. Unlike the spectrum, the autocorrelation function characterizes non-stationary noise as well as stationary noise so it is particularly suitable for signal dependent noise often found in disks. In addition, noise sources can be separated by properly choosing the sample space. Many interesting properties of particulate and metal film disks were found by this technique.     

基于小波变换的非平稳脉动风时变功率谱估计方法研究

为揭示非平稳随机脉动风的时频特性,基于小波变换原理推导了时变功率谱的时间、频率和幅值与小波变换系数的关系,建立了非平稳随机脉动风时变功率谱估计的小波函数加权和法,并采用模拟非平稳脉动风和实测台风过程对理论推导结果进行了验证。研究结果表明:非平稳随机过程在某一时刻的不同尺度小波变换系数是一个以此非平稳随机过程的调制函数与小波函数的乘积为调制函数的非平稳随机过程的傅里叶变换,非平稳随机过程的时变功率谱等于不同尺度和不同时移的小波函数模平方的加权和,小波函数加权和法计算的非平稳随机脉动风的时变功率谱与理论结果具有良好的一致性。小波函数加权和法可有效地估计非平稳随机脉动风的时变功率谱,估计的时变功率谱可为进一步理解强(台)风的随机脉动特性奠定基础。     

Sources of uncertainty in isotope ratio measurements by inductively coupled plasma mass spectrometry

A model is presented describing the effects of dead time and mass bias correction factor uncertainties, flicker noise, and counting statistics on isotope ratio measurement precision using inductively coupled plasma mass spectrometry (ICPMS) with a single collector. Noise spectral analysis is exploited to enable estimation of the flicker noise parameters. For the instrument used, the flicker noise component exhibited a fairly weak frequency (t) dependence (is proportional to f -0.33+/-0.12), but was directly proportional to the total number of counts, Q. As white noise, determined by counting statistics, is given by Q0.5, the isotope ratio measurement uncertainties will actually cease to improve when Q exceeds a certain threshold. This would suggest that flicker noise could become the limiting factor for the precision with which isotope ratios can be determined by ICPMS. However, under most experimental conditions, uncertainties associated with mass discrimination and dead time correction factors are decisive. For ratios up to approximately 22 (115In/113In), optimum major isotope count rates are generally below 0.3 MHz, for which precision in the mass discrimination factor is limiting. The model derived could be used as a starting point for determining optimum conditions and understanding the limitations of single-collector ICPMS for precise isotope ratio measurements.     

A low-flicker scheme for the real-time measurement of phase noise

This paper presents a new scheme for the measurement of phase noise in real time, based on carrier suppression and synchronous detection of the noise sidebands of the device being tested. In the instruments of the interferometric type, the carrier is suppressed by adding an equal and opposite signal that must be adjusted with a phase shifter and an attenuator. The proposed scheme makes use of a dual adjustment of the carrier suppression, coarse and fine. The former is by-step; the latter is continuous. Because of the higher stability of the by-step adjustment and the lower weight of the continuous adjustment in the suppression circuit, the instrument exhibits intrinsically low residual flicker and low microphonicity. A prototype shows a residual flicker as low as -160 dBrad/sup 2//Hz at 1 Hz off the 100 MHz carrier. Applications include the noise characterization of components and the design of innovative ultrastable oscillators.     

Estimations of frequency and its drift rate

This paper presents an analysis of frequency and its drift rate estimation by the difference method, the least-squares method, and the Kalman filter. Error formulas are derived for all five noise processes: white phase, flicker phase, white frequency, flicker frequency, and random walk frequency. The error formulas show the relationship between the estimate error and the noise spectral density coefficients, the same interval τ, and the data number N. Because of the existence of some nonstationary noise processes, a large data number may not yield a good estimation. One should choose an appropriate sample interval and data number so as to control the estimate error. An optimal solution based on the Kalman filter is presented     

Local oscillator limited frequency stability for passive atomic frequency standards using square wave frequency modulation

Atomic frequency standards using square wave frequency modulation effectively interrogate the atomic line by switching back and forth between two frequencies with equal atomic absorption values. For a symmetric absorption line, the slope of the responses will also be equal. In the quasistatic limit, this would seem to be an ideal interrogation process: the sign reversal of frequency slope can be removed by detection electronics to give an essentially unvarying sensitivity to local oscillator frequency variations. Such an interrogation would seem to eliminate L.O. aliasing and relieve stringent requirements on L.O. phase noise. Nevertheless, sign changes in the interrogation and detection processes mean that the sensitivity is actually zero at some point in the cycle. We derive consequences of this fact by an analysis in terms of the sensitivity function g(t). For white phase noise, we derive an optimal form for g(t) and show that the aliased noise always diverges as g(t) approaches a constant. For flicker phase noise, we find a limiting form that could, in principle, eliminate the aliasing effect; in practice, however, the improvement is limited by a slow dependence on available bandwidth. Finally, we derive optimized forms for any phase noise spectrum.