非线性网络Volterra级数表示的代数求解算法

本文基于非线性网络Volterra级数表示的辅助代数方法,提出了非线性网络n阶Volterra核和n阶非线性传递函数的代数编列算法。求取了非线性网络的规范形、三角形、对称形n阶Volterra核及相应的n阶非线性传递函数,同时也降低了非线性网络Volterra级数表示编列算法的复杂性。     

(n+1,m,2t)均衡弹性函数的非线性构造方法

基于GF(2)n上(n,m,2t-1)均衡弹性函数,运用其对偶分布性质和各分量函数弹性阶的相关特性,得到了(n 1,m,2t)均衡弹性函数的非线性构造方法。这些方法使得自变量的维数与弹性阶同步增长,且函数的代数次数也相应增加,从而避免了线性构造的缺陷。     

Tr（...）的二阶非线性度下界

作为影响系统安全的重要因素,对称密码中的密码函数应具有较高的r阶非线性度。对于r>1,目前对r阶非线性度的研究主要根据布尔函数微商的非线性度与其二阶非线性度之间的关系来进行。对于正整数n≡2（mod 4）,确定了一类布尔函数Tr(x^{2n/2+2n/2-1+1})的二阶非线性度下界。与相同变元数的两类已知布尔函数相比,研究的函数具有更紧的二阶非线性度下界。     

受驱动非线性幸福模型的动力学解析

基于Sprott幸福模型中的非线性期望模型,构建了受外界事件驱动的整数阶和分数阶非线性幸福模型。利用Ode-45算法和预估-校正法,分别对这两个非线性幸福模型进行了动力学解析。数值计算有效地展示了受外界事件驱动后的整数阶和分数阶非线性幸福模型有着更加丰富且复杂的非线性动力学现象。     

用第三代电流传送器设计n阶有源滤波器

提出了一种基于第三代电流传送器(CCIII)的电流模式n阶通用滤波器的设计方法,导出了设计公式,利用该方法可生成n阶高通、低通、带通滤波器,所产生的n阶滤波电路由n个CCIII+、2 n个无源元件构成。以二阶滤波器为例分析了高通、低通、带通滤波电路,结果显示各滤波电路的无源灵敏度和有源灵敏度都很低,以极点角频率106 ...     

非线性组合函数的相关免疫性在密码学上的应用

作为密码学上的应用,由几个线性反馈移位寄存器及一个非线性组合函数组成的伪噪声发生器己被建议用作流式密码中的密钥流(running key)发生器,有时,这些密钥流发生器能够被对其子序列的(唯密文)相关攻击所破译。现介绍一类新的组合函数,它能提供较好的保密性以对抗这样的攻击。其保密性由在相关攻击中要同时考虑的序列的最小数目m+1所确定。并证明了这样的m阶相关免疫性的一个必要条件。且给出一个递归构遣方法,对任意的m和n,1≤m相似文献   

镶嵌于介质中半导体纳米颗粒非线性光学性质的研究动态

介绍了有关镶嵌于介质半导体钠米颗粒非线性光学性质的研究动态，这种材料具准零维量子点特征，其三阶光学非线性系数大，响应快，功耗低，在光开关，光存储及全光逻辑运算等领域具有广阔的应用前景。     

高阶色散和五阶非线性下的交叉相位调制不稳定性

在同时考虑到光纤的二至四阶色散和三、五阶非线性的情况下,研究了四阶色散、五阶非线性以及入纤功率对双光束交叉相位调制(XPM)不稳定性的综合影响。研究表明,在高阶色散下,正负五阶非线性的存在仍然分别对交叉相位调制不稳定性起加强和削弱的作用;三阶色散对不稳定性增益谱无影响;当四阶和二阶色散系数同号时,四阶色散的存在导致交叉相位调制不稳定性增益谱出现一个新的远离零点的第二谱区,且该谱区由两个始终相连的小谱区组成;第一谱区的谱峰与第二谱区中靠近零点的小谱区的谱峰相当;随着其中一束光的入射功率的增加,两大谱区从分离到靠近再到合二为一,从三个谱峰过渡到两个谱峰;正(负)色散区的第二谱区中靠近(远离)零点的小谱区的谱峰和谱宽很小。在其他色散区时,不稳定性增益谱则只有第一或第二谱区。     

三五阶非线性下光纤中脉冲对的啁啾和频谱

为探究光纤的三五阶非线性对脉冲对频谱展宽的影响,从包含三五阶非线性的耦合非线性薛定谔方程出发,在忽略光纤色散和脉冲间走离效应的情况下,解析并计算模拟了高斯光脉冲对由于交叉相位调制所产生的非线性相移、频率啁啾,数值模拟了光脉冲对传榆中的功率频谱.结果表明:与只有三阶非线性相比,正五阶非线性使非线性相移和频率啁啾增大,而负五阶非线性则使非线性相移和频率啁啾减小甚至反号;正五阶非线性使脉冲频谱变宽,谱峰数目增多;绝对值较小的负五阶非线性使频谱变窄,谱峰数目减小,谱形变化,绝对值较大的负五阶非线性则展宽频谱,并使脉冲中心附近的谱峰变强.五阶非线性对功率相对较小的脉冲的影响更大些.此研究对超连续谱的产生、光开关器件、光脉冲压缩等研究都有一定的意义.     

光纤中5阶非线性效应对光脉冲传输的影响

为了研究5阶非线性效应对光脉冲在光纤中传输的影响,采用分步傅里叶算法数值求解了含5阶非线性项的扩展非线性薛定谔方程,并进行了理论分析和数值模拟。计算结果显示,负的5阶非线性效应使光脉冲峰值减小,脉冲展宽,正的5阶非线性效应使峰值增大,脉冲被压缩。较小的5阶非线性效应产生较小的调制不稳定性,因而光脉冲能保持基本的形状,忽略光纤的损耗时,光脉冲保持绝热传输。对正的5阶非线性效应,适当小的损耗可以减缓调制是不稳定性。结果表明,在5阶非线性系数固定的情况下,初始入射脉冲的峰值会显著地增加5阶非线性项的贡献。     

Averaging and Cancellation Effect of High-Order Nonlinearity of a Power Amplifier

Nonlinear distortion of a power amplifier (PA) due to the nonlinear input-output transfer function is studied. The high-order nonlinearity or Fourier components of the output, due to the mixing of input signals, are found to be related to an average integral related to the transfer function, thus giving insight to the cancellation effect of the nonlinearity. A simple formula has been derived to relate the nth-order Fourier component of a nonlinear transfer function with a sinusoidal input to an average integral of the nth-order derivative of the transfer function. The large signal nonlinear distortion of the nth-order can therefore be regarded as a weighted average of the nth-order derivative of the transfer function. For PAs, the averaging effect gives rise to local minima in the intermodulation distortion terms during power sweep because of the cancellation of the positive part and the negative part of the derivative during averaging. We have applied the formula to InGaP heterojunction bipolar transistors PAs and are able to explain most of the observed nonlinear phenomena of the amplifiers.     

On the boundedness of solutions of an nth-order time-lag system

A boundedness criterion is established between the solutions of an nth-order nonlinear functional differential equation and an nth-order nonlinear ordinary differential equation.     

AN ALGEBRAIC ALGORITHM TO VOLTERRA SERIES REPRESENTATION OF A NONLINEAR NETWORK

It is important to solve the nth-order Volterra kernel or nonlinear transfer function indescribing a nonlinear network by the Volterra series.Based on an auxiliary algebraic expression ofthe Volterra series,an algebraic algorithm is proposed to evaluate the nth-order Volterra kernel andnonlinear transfer function in regular,triangular and symmetric forms.In addition,the complexity ofthe algebraic algorithm is improved.     

Algorithm for solving a class of phase-lock-loop equations

An algorithm for solving the nonlinear Volterra equation of an nth-order phase-lock loop having all poles simple is presented. The proposed formulas are quite general with respect to the phase-detector nonlinearity and require little computational effort.     

The cumulant theory of cyclostationary time-series. I. Foundation

The problem of characterizing the sine-wave components in the output of a polynomial nonlinear system with a cyclostationary random time-series input is investigated. The concept of a pure nth-order sine wave is introduced, and it is shown that pure nth-order sine-wave strengths in the output time-series are given by scaled Fourier coefficients of the polyperiodic temporal cumulant of the input time-series. The higher order moments and cumulants of narrowband spectral components of time-series are defined and then idealized to the case of infinitesimal bandwidth. Such spectral moments and cumulants are shown to be characterized by the Fourier transforms of the temporal moments and cumulants of the time-series. It is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts. To put the contributions of the paper in perspective, a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided     

A theory of polyspectra for nonstationary stochastic processes

Harmonizable processes constitute an important class of nonstationary stochastic processes. We present a theory of polyspectra (higher order moment spectra) for the harmonizable class. We define and discuss four basic quantities: the nth-order moment function, the nth-order time-frequency polyspectrum, the nth-order ambiguity function, and the nth-order frequency-frequency polyspectrum. The latter generalizes the conventional polyspectrum to nonstationary stochastic processes. These four functions are related to one another by Fourier transforms. We show that the frequency and time marginals of the time-frequency polyspectrum are the instantaneous nth-order moment and the conventional nth-order stationary polyspectrum, respectively. All quantities except the nth-order ambiguity function allow for insightful interpretations in terms of Hilbert space inner products. The inner product picture leads to two novel and very powerful definitions of polycoherence for a nonstationary stochastic process. The polycoherences are objective measures of stationarity to order n, which can be used to construct various statistical tests. Finally, we give some specific examples and apply the theory to linear time-varying systems, which are popular models for fading multipath communication channels.     

一种新颖的电压模式N阶CFA低通滤波器的系统设计

提出了一种基于电流反馈放大器(CFA)的n阶电压模式多环反馈(multiple-loop feedback,简称MF)低通滤波器的系统设计方法,推导了系统的设计公式,利用该方法可导出n阶不同结构的低通滤波器,所产生的滤波器由n个CFA、n个电容、n个电阻构成。以三阶Butterworth低通滤波器为例阐述了设计过程,并用pspice进行仿真分析,设计和仿真结果表明,系统设计理论是正确的,设计方法是可行的。     

Designing multisine excitations for nonlinear model testing

This paper deals with the design of bandpass multisine excitations appropriate for microwave nonlinear model testing. A formal analysis showed that if the output power spectral density of a general nonlinear dynamic system is used as a metric for signal similarity, then it is possible to derive a set of statistical characteristics to be approximated. Using these nth-order extensions of the autocorrelation or the power spectral-density functions as the approximation goals, the multisine design problem is formulated as an optimization scheme where the various tone amplitudes and phases become the target design variables.     

Synthesis of transfer functions by dependent sources

A new procedure is given for the synthesis of nth-order voltage transfer functions by two dependent current sources as active elements. In the letter, by using a simple voltage-divider circuit configuration, the problem of the synthesis of transfer functions has been transformed to the synthesis of driving-point admittance functions.     

System reconstruction based on selected regions of discretizedhigher order spectra

We consider the problem of system reconstruction from arbitrarily selected slices of the nth-order output spectrum. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two one-dimensional (1-D) slices of the discretized nth-order output spectrum, (n⩾3), as long as the distance between the slices and the grid size satisfy a simple condition. For the special case of real systems, one slice suffices for system reconstruction. The ability to choose the slices to be used for reconstruction enables us to avoid regions of the nth-order spectrum, where the estimation variance is high, or where the ideal polyspectrum is expected to be zero, as is the case for bandlimited systems. We show that the obtained system estimates are asymptotically unbiased and consistent. We propose a mechanism for selecting slices that result in improved system estimates. We also demonstrate via simulations the superiority, in terms of estimation bias and variance, of the proposed method over existing approaches in the case of bandlimited systems