典型随机信号特征参数统计分布的分形特性

建立了一种能够描述随机信号结构基本特征的双参数脉冲信号统计模型.基于此模型,脉冲信号群幅度计数分布q(l_V),宽度计数分布p(l_τ)及给定宽度信号子集的幅度计数分布ε_lτ(l_V),给定幅度信号子集的宽度计数分布δ_lV(l_τ)均能很稳定的服从以序列自然数为自变量的对数正态分布.且计数分布的统计特征量μ_lnV,μ_lnτ,σ_lnV,σ_lnτ与信号的特征参数l_V,l_τ之间存在内在联系,这种联系的形式即随机信号分形特性的表现,表明随机信号特征参数的统计分布之间具有非整数维分形特征. 关键词： 分形 随机信号 双参数 统计     

颗粒群光散射脉冲信号统计参数分形特征

与不规则颗粒对应的随机脉冲信号计数分布是颗粒群粒度分布的完整反映。以幅度、宽度两个相对独立的特征参数为基础,研究了散射光脉冲信号计数分布的统计特性。利用激光尘埃粒子计数光电传感器对空气中尘埃粒子产生的散射光脉冲信号的幅度、宽度分布进行了统计测量,实验结果表明脉冲信号的统计分布不具有中心对称性,其幅度和宽度的计数分布都是满足对数正态分布规律。对数正态分布规律是测量过程中随机作用的具体表现。进一步的计算结果可证明,不规则颗粒群特征参数幅度和宽度之间存在分形结构关系,其分形维数为两者计数统计离散度的比值。     

带内干扰抑制的超宽带脉冲设计

采用不同幅度和延迟的高斯函数脉冲组合来拟合抽样函数脉冲,利用拟合的抽样函数脉冲设计超宽带脉冲信号,实现美国联邦通信委员会制定的辐射掩蔽要求的高效逼近.该方法产生的脉冲波形具有实现简单、持续时间短、带外辐射功率小、容易进行时域或频域调节等特点.与已报道的几种脉冲比较,设计的脉冲可携带更多的能量, 同时具有良好的带内（窄带或宽带）干扰抑制能力,能够和带内的其他通信系统更好的共存.最后,对设计的脉冲波形和最佳高斯波形的通信性能进行了比较,表明文中波形的性能明显优于最佳高斯波形.     

随机信号双参数脉冲模型的分形特征

为了研究随机信号的统计特性,以幅度、宽度两个相对独立的特征参数为基本概念,建立随机信号的双参数脉冲模型.采用PCI-9812高速数据采集卡,对空气中悬浮颗粒随机性光散射脉冲信号、光电传感器本底噪声随机信号进行计数分布的统计分析.实验结果表明,随机性脉冲信号幅度、宽度子集的计数分布以很高的精度与以自然数为自变量的对数正态分布符合;进一步的计算结果表明,在脉冲信号幅度、宽度定义域内,随机脉冲信号集合的两个特征参数之间存在非线性变换关系,即随机信号的双参数统计分布具有非整数维分形特征. 关键词： 分形 双参数 对数正态分布 随机脉冲信号     

基于Moreau包络平滑l_1/全变差范数模型的图像脉冲噪声去除方法

脉冲噪声是导致图像退化的主要原因之一,低密度脉冲噪声去除比较容易,但高密度比较困难。为了有效去除高密度的脉冲噪声,提高边缘和细节纹理的保持能力,提出了一种基于莫罗(Moreau)包络平滑l1/全变差范数(l1/TV)模型的脉冲噪声去除方法。此方法具有修复前后图像对比度和形态不变,不易产生局部模糊等优点。由于l1/TV模型中的两个目标函数均为不可微凸函数,无法直接求解,提出了利用解耦形式的Moreau包络对全变差范数进行平滑化处理,平滑后的函数是原函数的可微紧下界,具有迭代形式的解析解,证明了它也是原函数的解。仿真表明该算法具有很强的去噪能力,并能较好地保持边缘和细节信息。此外,还提出了该算法的加速策略,可以大大提高收敛速度。     

噪声信号特征量分布函数相似特性的研究

应用高速数据采集卡,记录悬浮颗粒计数光电传感器本底噪声信号序列值,研究噪声信号独立特征量, 如信号幅度极值、上升沿幅值、下降沿幅值、极值时序间隔,以及特征量乘积值等统计分布规律. 结果表明,上述独立特征量均能够与以自然数l为自变量的对数正态分布函数高度符合, 噪声信号特征量统计分布呈现出高度相似特征.基于这种统计相似性,还可推出噪声信号不同特征量对应的统计自变量之间的幂函数变换关系.噪声信号特征量统计分布函数相似性可理解为噪声信号集合统计分形特性的一种表现.     

面向脉冲量子级联激光器气体检测的锁相放大器

为了在基于脉冲式中红外量子级联激光器的气体检测系统中,精确提取窄脉冲传感信号的幅度,设计并实现了一种微秒级窄脉冲锁相放大器.根据微秒级窄脉冲的特点,窄脉冲信号经过窄带通滤波电路,得到基频正弦波信号,再经过主放大、移相、相敏检波电路,得到与脉冲幅值有关的直流信号.利用信号发生器产生的幅度、频率、相位可调的窄脉冲待测信号,对锁相放大器进行功能验证实验.结果表明,锁相放大器输出直流信号与输入信号的幅度呈良好的线性关系,线性拟合度约为98.043%;信号幅值的相对测量误差不超过3%;在1 h的测试时间内,信号波动范围在1‰以内.利用配备的不同浓度的一氧化碳样品及研制的锁相放大器,开展了一氧化碳气体检测实验.在0~180 ppm范围内,随着一氧化碳浓度的增加,锁相放大器的输出电压值与一氧化碳浓度呈现良好的e指数关系.根据A11an方差预测的系统检测下限为0.4123ppm.与商用锁相放大器相比,该放大器具有体积小、成本低、易于集成等特点,在基于脉冲式中红外量子级联激光器的气体检测中具有较好的应用前景.     

用于激光尾波场中电子束电荷测量的积分束流仪标定

 利用数字信号发生器及示波器对积分束流仪(ICT)的输入输出特性进行了标定,给出了不同脉冲宽度及幅度的输入信号与ICT输出结果的电荷量比值关系、输入脉冲对ICT的输出脉冲宽度的影响以及ICT对连续脉冲信号的输出响应等。标定结果显示:ICT的输入输出满足很好的线性关系;当输入连续脉冲的间隔小于一定程度时,ICT将会视为一个信号输出;ICT的输出脉冲形状及脉冲宽度与输入信号的形状及幅度无关。     

光电探测器随机噪声特征量统计分布函数

基于产生光电探测器噪声信号{V_i}的随机过程,分析了随机测量中稳定不变与随机涨落两部分的不同性质,建立了噪声信号随机性数学模型,分析得出在随机性统计研究中对统计分布函数的非线性约束关系.实验研究了同一随机过程中不同性质特征量随机涨落的统计计数规律,如随机噪声信号幅度值、极值幅度、极值间隔,相邻幅度差、乘积复合特征量、商复合特征量等随机特征量涨落统计分布规律均满足对数正态分布.从理论和实验上得出对数正态分布在描述随机过程中随机涨落部分性质的重要作用.     

激光应用 激光测量

P225.22006010233自动增益控制的自触发脉冲激光测距技术=Self-triggeringpulsedlaser rangefinding technology with automatic gain control[刊,中]/赵大龙(清华大学电子工程系.北京(100084)),秦来贵…∥激光与红外.—2005,35(8).—551-553提出了一种具有自动增益控制的自触发脉冲测距方案,不但减小脉冲信号上升沿引起的测距误差,而且也减小由于信号幅度变化带来的漂移误差影响。实验结果表明,该激光脉冲测距系统在1~10m的测距范围内,测距精度达到亚毫米级。图8参6(杨妹清)TH765.62006010234一种便携式激光测云仪的云底高度反演方法=Por…     

Spherical harmonics and cartesian tensor scalar product expansions of the distribution function

On the basis of the expansion of the distribution function in a sum of the spherical harmonics, the distribution functionf(v, r, t) is expanded in a series of scalar products of two Cartesian tensors term by term, i.e. The tensors and ^(l) (l=2, 3) are constructed in dependence on the spherical harmonic expansion coefficients (the tensors and ^(l) (l=0, 1) have been constructed by Jancel and Kahan [3]). On the basis of the knowledge of the analytic form off ₂ andf ₃ the equations forf ₁ f ₂ andf ₃ for the case of the Boltzmann's equation are determined.Technická 2, Praha 6, Czechoslovakia.     

Dual-mode optical fibres with zero intermodal dispersion

An exact analytical approach to the synthesis of the refractive-index profile of dual-mode optical fibres with zero intermodal dispersion is presented, and the computer-aided, trial-and-error synthesis of the optimal profile is described. The synthesis is based on inverse scattering theory. Self-consistency of free potentials corresponding to individual modes was attained by numerical methods. The characteristics of the optical fibres with synthetized profiles were analysed, the optimization constraints were specified, and an optimum profile was found. The results can be used for the design of broadband optical fibres.Notation (r), (r) Single and double derivatives - C _l(r) Determinant of a matrix det - k _l (r) Vector - k _l (r) _l (r) The scalar products of the vectors - K _l(wr) The modified Bessel function of the second kind - _l(wr) The modified Bessel function of the first kind - J _l(uaR) The Bessel function of the first kind     

A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

Almost Sure Weak Convergence for the Generalized Orthogonal Ensemble

The generalized orthogonal ensemble satisfies isoperimetric inequalities analogous to the Gaussian isoperimetric inequality, and an analogue of Wigner's law. Let v be a continuous and even real function such that V(X)=tracev(X)/n defines a uniformly p-convex function on the real symmetric n×n matrices X for some p2. Then (dX)=e ^–V(X) dX/Z satisfies deviation and transportation inequalities analogous to those satisfied by Gaussian measure^{(6, 27)}, but for the Schatten c ^p norm. The map, that associates to each XM ^s _n () its ordered eigenvalue sequence, induces from a measure which satisfies similar inequalities. It follows from such concentration inequalities that the empirical distribution of eigenvalues converges weakly almost surely to some non-random compactly supported probability distribution as n.     

Principle of limiting absorption for N-body Schrödinger operators — A remark on the commutator method

We consider a N-body Schrödinger operator H=H ₀+V. The interaction V is given by a sum of pair potentials V _jk(y)(=V _jk ^s +V _jk ^l ), y R³. We assume that: V _jk ^s =O(|y|^-(1+p)), p>0, as |y| for the short-range part V _jk ^s ; for the long-range part V _jk ^l . Under this assumption, we prove the principle of limiting absorption for H. The obtained result is essentially as good as those obtained in the two-body case. The proof is done by a slight modification of the remarkable commutator method due to Mourre.     

Probability distribution for percolation clusters generated on a cayley tree at criticality

We present analytical and numerical results for the probability distributions of the number of sitesS as a function of the number of shellsl for several ensembles of percolation clusters generated on a Cayley tree at criticality. We find that for the incipient infinite percolation cluster the probability distribution isP(S¦l)~(S/l ⁴)exp(- aS/l ²) for Sl1.     

A theoretical analysis of modulation noise and dc erased noise in magnetic recording

The modulation noise and the special case, dc erased noise in magnetic recording are discussed theoretically, taking account of two main causes at the same stage, i.e. the magnetic properties such as the inhomogeneous distribution of the particles on the tape, and the mechanical properties such as the head-to-tape space variations arising from the tape surface roughness. We derive the signal as well as the noise power spectrum of the induced voltage at the read head. This is done by generalizing the theory of the signal behaviour. The theoretical result turned out to agree quite well with the experimental one. The modulation noise power spectrum can be interpreted to consist of two parts, i.e. the steep peak due to the mechanical causes near the recorded signal wavenumber and the broad peak due to magnetic causes.Nomenclature A(k) variable defined by(Km_av L _g L _d)² - d head-to-tape spacing [m] - d _av average value ofd [m] - d variance ofd [m] - D variable defined by (8) - e(t) induced voltage at the read head [V] - g gap length [m] - H the Karlqvist head field excited by a current uniti [A/m] - i a curren unit [A] - j –1 - k=¦k¦ wavenumber [m^–1] - k _c wavenumber of recorded signal [m^–1] - K constant which includes the number of turn of head, the read head efficiency and the permeability ₀[Vs/Am] - l _d correlation length of the variationd [m] - l _m correlation length of the variationm [m] - L _d (k) spacing loss defined by exp(–kd_av) - L _g (k) gap loss defined by sin(gk/2)/(gk/2) - M magnetization of the tape [A/m] - M variable defined by (8) - m amplitude of the magnetization of the signal pattern [A/m] - m _av average value ofm [A/m] - m variance ofd [A/m] - P(k) power spectrum [V²/Hz] - P _dc(k) noise power spectrum [V²/Hz] - S signal pattern of the tape - v relative velocity between the head and the tape [m/s] - x _t =(x _t ,y_t) coordinate on the tape - (x ₀,y₀) coordinate fixed on the read head - (x ₁,y₁) coordinate defined by (10) - tape thickness [m] - _d random phase variable defined by (8) - _m random phase variable defined by (8) - _O permeability [Vs/Am] - read-head detected flux [Wb]     

Partial waves of a general off-shell two-body Coulomb-like T-matrix

On the basis of the Gell-Mann — Goldberger two-potential formalism we investigate the partial waves of an off-shell two-body T-matrix in the case of a general Coulomb-like potentialV=V _C +V _S . The regular kernelt _SC,l determining thel-th partial wave of the short-range partT _SC,l of the T-matrix is the solution of the equationt _SC,l =V _S,l +V _S,l G _C,l t _SC,l . The Lippmann-Schwinger operator of this equation formed by the short-range part of the potential and the pure Coulomb Green's operator is shown to be compact under very general assumptions on the potentialV _S admitting potentials vanishing in the coordinate representation liker ^–1– (>0) in the infinity. The special case of differentiable and analytic potentialsV _S,l (p,p) is considered in particular. The results are used to discuss in full generality the on-shell singularities of Coulomb-like T-matrices and wave functions and to investigate the singular integrals that occur in the Faddeev equations for Coulomb-like interactions.     

Cantor spectrum and singular continuity for a hierarchical Hamiltonian

We study the spectrum of the HamiltonianH onl ₂() given by (H)(n)=(n+1)+(n–1)+V(n)(n) with the hierarchical (ultrametric) potentialV(2 ^m (2l+1))=(1–R ^m )/(1–R), corresponding to 1-, 2-, and 3-dimensional Coulomb potentials for 0<R<1,R=1 andR>1, respectively, in a suitably chosen valuation metric. We prove that the spectrum is a Cantor set and gaps open at the eigenvaluese _n (1)<e _n (2)<...<e _n (2 ⁿ –1) of the Dirichlet problemH=E, (0)=(2 ⁿ )=0,n1. In the gap opening ate _n (k) the integrated density of states takes on the valuek/2 ⁿ . The spectrum is purely singular continuous forR1 when the potential is unbounded, and the Lyapunov exponent vanishes in the spectrum. The spectrum is purely continuous forR<1 in (H)[–2, 2] and =0 here, but one cannot exclude the presence of eigenvalues near the border of the spectrum. We also propose an explicit formula for the Green's function.Work supported by the Fonds National Suisse de la Recherche Scientifique, Grant No. 2.042-0.86 (H.K. and R.L.) and 2.483-0.87 (A.S.)On leave from the Dipartimento di Fisica, Università degli Studi di Firenze, Largo E. Fermi 2, I-50125 Firenze, Italy