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Losses and impulse response of a parabolic index fiber with random bends 随机弯曲抛物线折射率光纤的损耗和脉冲响应
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02026.X
D. Marcuse
The coupling coefficients of the modes of a parabolic index fiber with randomly curved axis are derived and are used to compute its excess losses and impulse response. It is found that bends with a period comparable to the natural ray oscillation period in the parabolic index medium are catastrophic. The average radius of curvature R c of a guide composed of circular sections with an average length of 1 cm must not decrease below approximately R c = 1 m. Mode coupling by random bends has the tendency to reduce the width of the impulse response function. However, this improvement is accompanied by losses. Reducing the width of the impulse response for coupled mode operation to half its uncoupled width causes 0.7 dB additional loss, a ten-fold reduction of the pulse width costs 18 dB.
导出了具有随机弯曲轴的抛物折射率光纤的模态耦合系数,并用于计算光纤的超损耗和脉冲响应。在抛物线折射率介质中,周期与自然射线振荡周期相当的弯曲是灾难性的。由平均长度为1厘米的圆截面组成的导轨,其平均曲率半径rc不得小于约rc = 1米。随机弯曲的模态耦合有减小脉冲响应函数宽度的趋势。然而,这种改善伴随着损失。将耦合模式工作的脉冲响应宽度减小到非耦合宽度的一半会导致0.7 dB的额外损失,而将脉冲宽度减小10倍则需要18 dB。
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引用次数: 83
Use of a gate to reduce the variance of delays in queues with random service 使用门来减少随机服务队列中的延迟方差
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02025.X
R. D. Coleman
We consider an N-server queuing system with Poisson arrivals and exponential service, in which arriving customers must pass through a gate into a waiting room before becoming eligible for service. Customers who find the gate closed wait outside until the gate opens; customers inside the waiting room are served at random. When the last customer inside acquires a server, the gate admits all those outside and then closes again. If no customer is waiting outside when the gate opens, the gate remains open until there is a queue of k waiting customers. Service offered by this system is intermediary between random service and order-of-arrival service. As long as the gate is open and fewer than N + k customers are in the system, service is purely random. The parameter k can be regarded as a threshold at which the queue is judged too long to permit random service to continue. Our main results are (i) the Laplace-Stieltjes transform of the equilibrium distribution of the waiting time of an arbitrary customer and (ii) a comparison of the second moments of the waiting time for different values of k with those of the waiting time under random service and order-of-arrival service. The service is shown to be “nearly random” at low loads and “not quite order-of-arrival” at high loads; for higher values of k this transition occurs at higher traffic intensities.
我们考虑一个具有泊松到达和指数服务的n服务器排队系统,其中到达的客户必须通过一个门进入等候室才有资格获得服务。发现大门关闭的顾客在门外等候,直到大门打开;等候室里的顾客是随机得到服务的。当内部的最后一个客户获得服务器时,大门允许所有外部的客户进入,然后再次关闭。如果在大门打开时没有顾客在外面等候,那么大门将一直打开,直到有k个顾客排队等候。该系统提供的服务是随机服务和到货服务之间的中介。只要大门是开着的,并且系统中的客户少于N + k,服务就完全是随机的。参数k可以看作是一个阈值,在这个阈值上,判断队列太长而不允许随机服务继续。我们的主要成果是:(i)任意顾客等待时间均衡分布的Laplace-Stieltjes变换和(ii)不同k值下等待时间的第二矩与随机服务和到达顺序服务下等待时间的第二矩的比较。该服务在低负载时“几乎是随机的”,在高负载时“不完全是按顺序到达的”;对于较高的k值,这种转变发生在较高的交通强度。
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引用次数: 3
Volterra systems with more than one input port — distortion in a frequency converter 变频器中有多个输入端口的Volterra系统
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02019.X
S. Rice
Consider a nonlinear system, with memory, which has two input ports and one output port. It is assumed that the system can be represented by a double Volterra series. Two results for such a system are stated in Part I. The first is a general expression for the sinusoidal components of the output y (t) when the two inputs x u (t) and x v (t) are sums of sinusoidal terms. The second result is an expression for the power spectrum of y (t) when x u (t) is a stationary Gaussian process and x v (t) = P cos pt. Part II is concerned with using results from the theory of Volterra series for multi-input systems to calculate the third-order distortion in an idealized frequency converter.
考虑一个有内存的非线性系统,它有两个输入端口和一个输出端口。假设系统可以用双Volterra级数表示。第一部分给出了这样一个系统的两个结果。第一个是当两个输入x u (t)和x v (t)是正弦项的和时,输出y (t)的正弦分量的一般表达式。第二个结果是当x u (t)是平稳高斯过程且x v (t) = pcos pt时y (t)的功率谱的表达式。第二部分涉及使用多输入系统Volterra级数理论的结果来计算理想变频器中的三阶失真。
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引用次数: 23
The metallurgy of remendur: Effects of processing variations 金属冶金:工艺变化的影响
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02022.X
M. Pinnel, J. Bennett
A recent development effort in telecommunications switching apparatus has been directed toward the production of a remanent reed, dry, sealed contact (remreed). Remendur, a medium-hard magnetic alloy nominally composed of equal parts iron and cobalt and 2.7-wt. percent vanadium, was chosen as the reed material in this contact. However, the application required the alloy to possess rather specific magnetic and mechanical properties and considerable difficulty was experienced in consistently processing Remendur into wire with these specified properties. To ascertain the sensitivity of these properties to variations in processing times and temperatures, and vanadium content, two melts of Remendur (2.5-percent V and 3.0-percent V) were processed with selected alterations in annealing temperatures at several stages. Microstructures were characterized following each step by light microscopy and were correlated with the appropriate ternary equilibrium diagram. Results demonstrate that microstructures developed by anneals between 900°C and 950°C are extremely sensitive to the precise temperature of the anneal and composition of the alloy. The microstructure, which strongly influences magnetic and mechanical properties, can be varied over the limits of the two-phase α 1 + γ region by variations in vanadium content of only 0.5 wt. percent and by the small 50°C temperature range.
最近在电信交换设备方面的一项开发工作是针对残余簧片、干的、密封的触点的生产。这是一种中硬磁性合金,名义上由等量的铁和钴组成,重2.7吨。在这个触点中,选择百分之钒作为簧片材料。然而,该应用要求合金具有相当特定的磁性和机械性能,并且在将Remendur持续加工成具有这些特定性能的线材方面经历了相当大的困难。为了确定这些性能对加工时间和温度以及钒含量变化的敏感性,在几个阶段对两种remendr熔体(2.5% V和3.0% V)进行了退火温度的选择。在光镜下对每一步的微观结构进行了表征,并与相应的三元平衡图相关联。结果表明,在900 ~ 950℃之间退火形成的组织对退火温度和合金成分极为敏感。对磁性和机械性能有强烈影响的微观结构可以在两相α 1 + γ区域的极限上发生变化,钒含量的变化仅为0.5 wt. %,温度范围为50°C。
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引用次数: 22
Effect of misalignments on coupling efficiency of single-mode optical fiber butt joints 错位对单模光纤对接耦合效率的影响
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02027.X
J. Cook, W. Mammel, R. Grow
Analysis and computations made here, corroborated by experiment, determine the effects of axial displacement and angular misalignment on the power coupled between butt-joined, single-mode optical fibers. The absolute accuracy with which fibers must be joined on-centers is reduced for fibers with relatively smaller core; the angular accuracy is increased.
本文的分析和计算得到了实验的证实,确定了轴向位移和角不对中对对接单模光纤间功率耦合的影响。对于纤芯相对较小的纤维,必须在中心连接的绝对精度会降低;提高了角度精度。
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引用次数: 43
Picture coding: The use of a viewer model in source encoding 图片编码:在源代码编码中使用查看器模型
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02020.X
J. Limb
A method is suggested for inserting viewer criteria directly into coding algorithms; any complex visual model may be used. The technique is applied to a DPCM-type coder, and a number of variations are compared on the basis of entropy, quality, and complexity. It is found that, using a simple one-dimensional filter model, the first-order entropy of the DPCM signal can be reduced by 30 percent for a high-detail picture with only a small reduction in picture quality. Furthermore, by means of a single threshold control, one can efficiently trade off bit-rate and picture quality over a large range for use in adaptive strategies.
提出了一种将查看器准则直接插入编码算法的方法;任何复杂的可视化模型都可以使用。该技术应用于dpcm型编码器,并在熵、质量和复杂性的基础上比较了许多变体。我们发现,使用一个简单的一维滤波模型,DPCM信号的一阶熵可以减少30%的高细节图像,而图像质量只有很小的下降。此外,通过单一阈值控制,可以有效地在大范围内权衡比特率和图像质量,以用于自适应策略。
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引用次数: 10
Statistical properties of gilbert's burst noise model 吉尔伯特突发噪声模型的统计特性
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02021.X
M. Chao
Simple statistical procedures for analyzing error data, e.g., in digital data transmission systems, are usually based on the assumption of independence. This paper studies the performance and potential utility of such simple statistical procedures in the case of nonindependent error occurrences. The burst noise model is selected for this purpose because of its neatness, its mathematical tractability, its built-in structure of dependence, and its importance in communication theory. We show that statistical procedures designed under the assumption of independence tend to be conservative for the burst noise model. For example, the usual binomial test will reject, on the average, more channels with small error rates than it would if the errors were independent. The case that the sample size n and the error rate ρ converge in such a way that nρ→ µ 0 is also studied. It is shown that the error process can be approximated by a compound Poisson process in continuous time t. The statistical implications of this fact are also discussed.
分析误差数据的简单统计程序,例如在数字数据传输系统中,通常以独立性假设为基础。本文研究了这种简单的统计程序在非独立错误发生情况下的性能和潜在效用。选择突发噪声模型是由于它的整洁性、数学上的可跟踪性、内在的依赖结构以及它在通信理论中的重要性。我们发现,在独立假设下设计的统计程序对于突发噪声模型往往是保守的。例如,通常的二项检验将平均拒绝更多具有小错误率的信道,而不是如果错误是独立的。还研究了样本量n和错误率ρ以使nρ→µ0的方式收敛的情况。结果表明,误差过程可以用连续时间t的复合泊松过程来近似,并讨论了这一事实的统计意义。
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引用次数: 2
Optimum mean-square decision feedback equalization 最优均方决策反馈均衡
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02023.X
J. Salz
In this work we report new results relating to decision feedback equalization. The equalizer and the transmitting filter are optimized in a PAM data communication system operating over a linear noisy channel. We use a mean-square error criterion and impose an average power constraint at the transmitter. Assuming correct past decisions, an explicit formula for the minimum attainable mean-square error is given. The possible advantages of signaling faster than the Nyquist rate while decreasing the number of levels to maintain the same information rate are investigated. It is shown that, in all cases of practical interest, signaling faster than the Nyquist rate, while keeping fixed the information rate, increases the mean-square error. Finally, to illustrate the use of the results, application is made to a cable channel where the loss in dB varies as the square root of frequency. Various asymptotic formulas and curves are provided to exhibit the relationships between the quantities of interest.
在这项工作中,我们报告了有关决策反馈均衡的新结果。对工作在线性噪声信道上的PAM数据通信系统中的均衡器和发射滤波器进行了优化。我们使用均方误差准则并对发射机施加平均功率约束。假设过去的决策是正确的,给出了最小均方误差的显式公式。研究了以比奈奎斯特速率更快的速度发送信号,同时减少电平数以保持相同的信息速率的可能优势。结果表明,在所有实际情况下,在保持信息速率不变的情况下,比奈奎斯特速率更快的信号会增加均方误差。最后,为了说明结果的使用,将其应用于一个以dB为单位的损耗随频率的平方根而变化的电缆信道。提供了各种渐近公式和曲线来显示感兴趣的量之间的关系。
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引用次数: 344
Traffic measurement biases induced by partial sampling 部分抽样引起的交通测量偏差
Pub Date : 1973-10-01 DOI: 10.1002/J.1538-7305.1973.TB02024.X
A. Descloux
Under equilibrium conditions, the sample average of the delays encountered by all the calls submitted during a given time interval is an unbiased estimate of the mean of the delay distribution. If some of the delays are not observed, the resulting sample average need no longer be an unbiased estimator of the corresponding population mean. This is the case when, for instance, only a limited number of delays can be timed simultaneously. The purpose of this paper is to investigate these biases for queuing systems when only one clock is available and thus one delay only can be measured at a time. It is shown that, regardless of the order of service, the expected value of the observed average delays is always smaller than the mean waiting time for all calls. Although the average delay on all calls is independent of the order of service, the measurement biases resulting when only one delay can be measured at once depend on the queue discipline. In particular, we shall show that the average delay for all calls is always larger than the average delay of the observed calls even if these calls are always served last (observed-call served-last).
在均衡条件下,在给定的时间间隔内,所有呼叫所遇到的延迟的样本平均值是延迟分布平均值的无偏估计。如果没有观察到某些延迟,则得到的样本平均值不再需要是相应总体平均值的无偏估计量。例如,只有有限数量的延迟可以同时计时。本文的目的是研究当只有一个时钟可用时排队系统的这些偏差,因此一次只能测量一个延迟。结果表明,无论服务顺序如何,观察到的平均延迟的期望值总是小于所有呼叫的平均等待时间。尽管所有呼叫的平均延迟与服务顺序无关,但是当一次只能测量一个延迟时产生的测量偏差取决于队列规则。特别是,我们将证明所有呼叫的平均延迟总是大于观察到的呼叫的平均延迟,即使这些呼叫总是最后服务(观察到的呼叫服务的最后)。
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引用次数: 1
Heuristic solution of a signal design optimization problem 信号设计优化问题的启发式求解
Pub Date : 1973-09-01 DOI: 10.1002/J.1538-7305.1973.TB02009.X
B. Kernighan, S. Lin
This paper discusses a heuristic solution procedure for a combinatorial optimization problem that originates in designing signal constellations for modems. The design problem is to place m signals in a two-dimensional space to minimize the average error rate under specified noise conditions, using a maximum-likelihood decoding scheme. Intuitively, it amounts (roughly) to spreading the signal points as far apart as possible, according to the distance measurement implied by the noise function. We show how this problem can be reduced to a discrete one: Given an l by n matrix P, and m 1 , …, i m } of the rows of P that maximizes and then describe an efficient procedure for finding this maximizing set. Experiments indicate that the procedure is a useful tool, both for analysis of existing and proposed signal constellations and for finding new, near-optimum ones.
本文讨论了在调制解调器信号星座设计中出现的组合优化问题的启发式求解过程。设计问题是将m个信号放置在二维空间中,在规定的噪声条件下,使用最大似然解码方案最小化平均错误率。直观地说,它(大致)相当于根据噪声函数所隐含的距离测量,将信号点尽可能地分散开来。我们展示了如何将这个问题简化为一个离散的问题:给定一个l × n矩阵P,以及P中最大的行的m1,…,im},然后描述一个寻找这个最大集的有效过程。实验表明,该方法对于分析现有的和提出的信号星座以及寻找新的、接近最优的信号星座都是一个有用的工具。
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引用次数: 15
期刊
Bell System Technical Journal
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