Showing papers in "Bell System Technical Journal in 1962"
TL;DR: In this paper, the authors examined the mathematical truth in the engineering intuition that there are approximately 2WT independent signals ϕ i of bandwidth W concentrated in an interval of length T. Roughly speaking, the result is true for the best choice of the ϕ I (prolate spheroidal wave functions), but not for sampling functions (of the form sin t/t).
Abstract: The purpose of this paper is to examine the mathematical truth in the engineering intuition that there are approximately 2WT independent signals ϕ i of bandwidth W concentrated in an interval of length T. Roughly speaking, the result is true for the best choice of the ϕ i (prolate spheroidal wave functions), but not for sampling functions (of the form sin t/t). Some typical conclusions are: Let f(t), of total energy 1, be band-limited to bandwidth W, and let $\int_{-t/2}^{t/2} \vert f^{2}(t)\vert dt = 1- \epsilon_{T}^{2}$ . Then ${\rm inf}\limits_{\{a_{i}\}} \int_{-\infty}^{\infty} \left\vert f(t)- \sum_{0}^{[2WT]+N]} a_{n}\varphi_{n}\right\vert^{2} dt \lt C_{\epsilon_{T}^{2}}$ is (a) true for all such f with N = 0, C = 12, if the ϕ n are the prolate spheroidal wave functions; (b) false for some such f for any finite constants N and C if the ϕ n are sampling functions.
1,123 citations
TL;DR: In this paper, the authors considered the probability that a stationary Gaussian process with mean zero and covariance function r(τ) be nonnegative throughout a given interval of duration T. Several strict upper and lower bounds for P were given, along with some comparison theorems that relate P's for different covariance functions.
Abstract: This paper is concerned with the probability, P[T, r(τ)], that a stationary Gaussian process with mean zero and covariance function r(τ) be nonnegative throughout a given interval of duration T. Several strict upper and lower bounds for P are given, along with some comparison theorems that relate P's for different covariance functions. Similar results are given for F[T, r(τ)], the probability distribution for the interval between two successive zeros of the process.
786 citations
TL;DR: In this paper, the resistivity and impurity concentration in heavily doped silicon are reported and incorporated in a graph showing the resistivities (at T = 300°K) of n-and p-type silicon as a function of donor or acceptor concentration.
Abstract: Measurements of resistivity and impurity concentration in heavily doped silicon are reported. These and previously published data are incorporated in a graph showing the resistivity (at T = 300°K) of n- and p-type silicon as a function of donor or acceptor concentration. The relationship between surface concentration and average conductivity of diffused layers in silicon has been calculated for Gaussian and complementary error function distributions. The results are shown graphically. Similar calculations for subsurface layers, such as a transistor base region, are also given.
580 citations
TL;DR: In this paper, the theory of the confocal resonator was extended to include the effect of unequal aperture size and unequal radii of curvature of the two reflectors, which is equivalent to a periodic sequence of lenses with unequal focal lengths.
Abstract: The theory of the confocal resonator is extended to include the effect of unequal aperture size and unequal radii of curvature of the two reflectors. The latter is equivalent to a periodic sequence of lenses with unequal focal lengths. This treatment is in Cartesian coordinates as previously used. In an appendix the modes and resonant formulas are written in cylindrical coordinates. The effect of unequal aperture size of the two reflectors is shown to produce mode patterns of unequal size on the two reflectors of a confocal resonator. The previous computations for diffraction losses are found to be applicable. Generalization of the theory to the case of reflectors of unequal curvature shows the existence of low-loss regions and high-loss regions as the reflector spacing is varied. One of the high diffraction loss regions occurs when the reflector spacing is between the two unequal radii of curvature. Such a region is interpretable in terms of instabilities in a periodic sequence of lenses of unequal focal length. An estimate of diffraction losses is obtained for the low-loss regions. The presence of a high diffraction loss region or unstable region should be of importance in the design of resonators or of a periodic sequence of lenses.
473 citations
TL;DR: The construction of non-computable functions used in this paper is based on the principle that a finite, non-empty set of nonnegative integers has a largest element as mentioned in this paper, and this principle is used only for sets which are exceptionally well-defined by current standards.
Abstract: The construction of non-computable functions used in this paper is based on the principle that a finite, non-empty set of non-negative integers has a largest element. Also, this principle is used only for sets which are exceptionally well-defined by current standards. No enumeration of computable functions is used, and in this sense the diagonal process is not employed. Thus, it appears that an apparently self-evident principle, of constant use in every area of mathematics, yields non-constructive entities.
286 citations
TL;DR: A class of three-stage connecting networks proven rearrangeable by D. Slepian is considered and bounds on the number of calls that must be moved are obtained by some simple new methods.
Abstract: A class of three-stage connecting networks proven rearrangeable by D. Slepian is considered. Bounds on the number of calls that must be moved are obtained by some simple new methods.
209 citations
TL;DR: In this article, the performance of a thermally grown oxide on silicon was analyzed and measurements made on several experimental units were described, and a theory developed from the surface charge relation was shown to agree with the experimental data over a wide range of silicon resistivity.
Abstract: The semiconductor varactor using surface space charge is analyzed and measurements made on several experimental units are described. The chief characteristics of this device are its capacity-voltage dependence and its negligible dc conduction. The particular system used in this work is a thermally grown oxide on silicon. A theory developed from the surface charge relation is shown to agree with the experimental data over a wide range of silicon resistivity. The theory for optimum operation for both dc and ac biasing is derived and used to compare the performance of this device with that of the p-n junction varactor. The result of this comparison shows that with careful design the semiconductor surface varactor will be able to compete favorably with the junction varactor for many possible applications, including those of ultra high frequency.
119 citations
TL;DR: In this paper, the usual Fabry-Perot interferometer structure of the optical maser was modified in a very simple way to provide discrimination against unwanted orders, which can greatly affect the losses of the various orders.
Abstract: It is proposed here that the usual Fabry-Perot interferometer structure of the optical maser may be modified in a very simple way to provide discrimination against unwanted orders. The modification is an extra reflecting surface suitably positioned outside the maser which can greatly affect the losses of the various orders. A simple one-dimensional analysis is given for the effect, and numerical results are presented for a realistic case, showing that the effect can be large. It is concluded that this technique may be useful in preventing unwanted oscillations in the optical maser.
105 citations
TL;DR: One important nonparametric result is that the proportion of the total sample used for testing the machine should never be less than that proportion used for designing the machine, and in some cases should be a good deal more.
Abstract: A popular procedure for testing a pattern recognition machine is to present the machine with a set of patterns taken from the real world. The proportion of these patterns which are misrecognized or rejected is taken as the estimate of the error probability or rejection probability for the machine. In Part I, this testing procedure is discussed for the cases of unknown and known a priori probabilities of occurrence of the pattern classes. The differences between the tests that should be made in the two cases are noted, and confidence intervals for the test results are indicated. These concepts are applied to various published pattern recognition results by determining the appropriate confidence interval for each result. In Part II, the problem of the optimum partitioning of a sample of fixed size between the design and test phases of a pattern recognition machine is discussed. One important nonparametric result is that the proportion of the total sample used for testing the machine should never be less than that proportion used for designing the machine, and in some cases should be a good deal more.
103 citations
TL;DR: In certain types of connection networks, it is always possible to unblock a blocked call by moving calls already set up in the network by using methods of systematically changing connections.
Abstract: In certain types of connection networks, it is always possible to unblock a blocked call by moving calls already set up in the network. The following results relating to these networks are derived in this article. 1. Bounds on the number of calls which must be disturbed to unblock a blocked call. 2. Bounds on the relation between the number of calls which are already set up in the network, and the number of calls that must be disturbed to unblock a blocked call. 3. Methods of systematically changing connections to unblock a blocked call.
98 citations
TL;DR: In this paper, a code and repeater structure for reconstructing this code to minimize the effect of crosstalk into the timing channel of a reconstructive repeater is emphasized.
Abstract: Attention is focused on the choice of a code for transmitting a PCM signal in the exchange plant via paper-insulated cable pairs. Inter- and intra-system crosstalk via near-end coupling is the principal source of interference. A code and repeater structure for reconstructing this code to minimize the effect of crosstalk into the timing channel of a reconstructive repeater is emphasized. It is shown that the conventional self-timed unipolar repeater is not suited to this environment. Several pseudo-ternary codes are developed and surveyed for overcoming crosstalk interference. A bipolar code and a repeater for reconstructing this code are chosen for a variety of reasons. The repeater features nonlinear timing wave extraction and complete retiming and pulse width control, and its realization is discussed in detail in a companion paper by J. S. Mayo.3
TL;DR: In this paper, the effects of random geometric imperfections on the transmission of the TE 01 wave in circular waveguide are studied; the necessary theory of guides with known arbitrary imperfections is first developed.
Abstract: The effects of random geometric imperfections on the transmission of the TE 01 wave in circular waveguide are studied; the necessary theory of guides with known arbitrary imperfections is first developed. The TE 01 transmission statistics are determined in terms of the statistics of the various types of geometric imperfections. Both discrete mode converters — i.e., localized imperfections such as tilts, offsets, or diameter changes at joints between pipes that are perfect right-circular cylinders — and continuous geometric imperfections — such as straightness deviation, diameter variation, ellipticity, etc., that vary smoothly with distance along the guide — are considered. The average, variance, power spectrum, and probability distribution of the TE 01 loss-frequency curve are discussed. Continuous straightness deviation (of the individual pipes of the guide) appears to be the most serious tolerance in present copper waveguide, and a significant factor in helix guide as well. The power spectrum of the straightness deviation is all-important in determining the TE 01 loss due to mode conversion. Fourier components of straightness deviation having wavelengths between roughly 1.4 and 4.4 feet are the significant ones for the present 2-inch I.D. guide operated in a frequency band from 35 to 90 kmc.
TL;DR: Property of the phase-controlled oscillator with a sawtooth comparator that have been mentioned in the literature for sinusoidal comparators are analyzed and there is new theoretical material on the effect of fast jitter and noise.
Abstract: A sawtooth phase comparator has advantages over the more common sinusoidal comparator in a phase-controlled oscillator because its output is linear for larger values of phase error. For some applications, it is no more complex or expensive than the sinusoidal comparator. This paper analyzes properties of the phase-controlled oscillator with a sawtooth comparator that have been mentioned in the literature for sinusoidal comparators. In addition, there is new theoretical material on the effect of fast jitter and noise. The properties of the circuit are presented in a manner which is convenient for design. Since it is easier to analyze the circuit with a sawtooth comparator, many applications of the device have been considered. Because of this wide viewpoint, the paper may be helpful in understanding the phase-controlled oscillator in general.
TL;DR: In this paper, the basic ideas leading to a unidirectional traveling-wave optical maser are presented, and experimental data on the performance of pulsed ruby amplifying sections and high density PbO glass Faraday rotation isolators are given.
Abstract: The basic ideas leading to a unidirectional traveling-wave optical maser are presented. Experimental data on the performance of pulsed ruby amplifying sections and high density PbO glass Faraday rotation isolators are given. Feasibility tests on a two-section device have been made and are in agreement with predictions. Some remarks are made concerning image definition, channel capacity, noise and pump power requirements.
TL;DR: In this paper, the electron-beam method was used to determine the diffusion length of solar cells with high-energy electrons, heavy particles, and gamma rays in silicon solar cells.
Abstract: Penetrating radiation in the form of high-energy electrons, heavy particles, and gamma rays may be used to determine minority-carrier diffusion lengths in semiconductor materials containing junctions by measuring the radiation-induced short circuit current. The electron-beam method yields an accurate absolute determination of diffusion length once the carrier-generation rate as a function of depth in the material has been measured. A series of such experiments is described for silicon solar cells utilizing electrons ranging in energy from 0.61 Mev to 1.16 Mev. A resultant maximum generation rate of 2.25 × 106 ± 5 per cent carriers/cm per incident 1 Mev electron is obtained at a depth of 0.096 gm/cm2. Measurements with 16.8 Mev and 130 Mev protons, and Co60 gamma rays are found to be in good agreement with the electron-beam measurements. An experimental arrangement is described which yields rapid and accurate diffusion-length measurements of solar cells under conditions in which radiation damage is negligible.
TL;DR: In this article, a formula for the probability of stimulated emission of Bremsstrahlung is derived and it is shown that stimulated emission occurs if the incident electrons travel in a direction roughly parallel to the electric field vector of the wave stimulating the emission.
Abstract: A formula for the probability of stimulated emission of Bremsstrahlung is derived. It is shown that stimulated emission occurs if the incident electrons travel in a direction roughly parallel to the electric field vector of the wave stimulating the emission. Emission from free electrons is used in electron tube devices. The purpose of this paper is to show that stimulated emission occurs already in the elementary process of the encounter of one electron and one nucleus or ion. There is no need for a slow-wave structure or elaborate electron bunching and no need to consider phase relationships. This elementary effect of stimulated emission should lead to a type of oscillator and broadband amplifier working without slow-wave structures or need for the close mechanical tolerances of high-frequency klystrons. A device of this kind may be noisier than a conventional maser. It may be that the effect discussed in this paper is responsible for some of the hitherto unexplained semiconductor diode oscillations which have been reported in the literature.
TL;DR: In this article, a two-way repeater was developed for use on unloaded exchange cable, which was designed to satisfy the transmission requirements of an experimental PCM system, and it utilizes a pulse repetition frequency of 1.544 cm and a 6000-ft repeater spacing.
Abstract: Designed for use on unloaded exchange cable, this repeater was developed to satisfy the transmission requirements of an experimental PCM system. It utilizes a pulse repetition frequency of 1.544 mc, and 6000-ft repeater spacing. Functionally, the repeatered line transmits the PCM signal without appreciable degradation over distances up to 25 miles, a feat accomplished by retiming and reshaping the signal at each repeater point. Retiming is accomplished by means of a clock extracted from the signal; reshaping is accomplished by regeneration with positive pulse width control. Near-end crosstalk and pulse train jitter dominate the design parameters. Timing is made tolerant of near-end crosstalk by choice of bipolar transmission (where successive marks are of opposite polarity) with clock derived from the rectified and clipped signal. Tolerance in the decision circuit is obtained by automatic threshold control, spike sampling, and tight control of time and voltage parameters. Accumulated pulse train jitter is controlled to the extent dictated by the terminal equipment, principally through control of the bandwidth of the clock circuit. Seven diffused-base transistors and ten logic diodes are used in the oneway repeater circuit. A two-way repeater consists of two such circuits with a common power unit, utilizes 135 components, and is packaged in a can of $1{1 \over 16} x 3{1 \over 8} x 5{3\over 4}$ -inches outside dimensions. Accommodations are made for line-length and power options, as well as remote testing. Power for the repeater is transmitted over the signal pair. One watt is required for the two-way repeater.
TL;DR: A comprehensive view of the theory of connecting systems is presented, an appraisal of its current status, and some suggestions for further progress are made.
Abstract: A connecting system consists of a set of terminals, a control unit for processing call information, and a connecting network. Together, these three elements provide communication, e.g., supply telephone service, among the various terminals. In this paper we present a comprehensive view of the theory of connecting systems, an appraisal of its current status, and some suggestions for further progress. The existing probabilistic theory is reviewed and criticized. The basic features of connecting systems, such as structure, random behavior, complexity, and performance, are discussed in a nontechnical way, and the chief difficulties that beset the construction of a theory of traffic in large systems are described. It is then pointed out that despite their great complexity, connecting systems have a definite structure which can be very useful in analyzing their performance. A natural division of the subject into combinatory, probabilistic, and variational problems is drawn, and is illustrated by discussing a simple problem of each type in detail.
TL;DR: The TASI (Time Assignment Speech Interpolation) has been in service on transatlantic submarine cable channels since mid-1960 and has been evaluated in this article, showing that performance equals or exceeds the original engineering objectives in all but a few cases.
Abstract: TASI (Time Assignment Speech Interpolation) has been in service on transatlantic submarine cable channels since mid-1960. Measurement of service quality on one TASI system (White Plains-London) indicates that system performance equals or exceeds the original engineering objectives in all but a few cases. Field modifications now being made should bring these exceptions into closer agreement with objectives. A companion paper4 discusses in detail the design considerations for TASI speech detectors and describes subjective tests made to determine the maximum permissible loading of TASI circuits without impairment of service.
TL;DR: In this paper, the second half of results of a study on the peripheral ear were presented, where the authors derived computational models for approximating the mechanical displacement of the basilar membrane when the sound pressure at the eardrum is known.
Abstract: This report presents the second half of results of a study on the peripheral ear. There are two objectives: (1) to derive computational models for approximating the mechanical displacement of the basilar membrane when the sound pressure at the eardrum is known, and (2) to demonstrate certain relations between subjective behavior measured experimentally and physiological behavior calculated from the models. The report describes a rational function approximation of middle-ear transmission. This result, in combination with previously derived models for the inner ear, permits an analytical approximation of basilar membrane displacements in both apical and basal regions. Because the models are rational functions, they can, if desired, be simulated by lumped-constant electrical networks. Their computational tractability also permits straightforward approximations to temporal and spatial derivatives of displacement. Relations between computed membrane displacement and subjective behavior are illustrated for several psycho-acoustic phenomena, namely pitch perception, binaural lateralization, binaural time-intensity trade, threshold discrimination, and pure-tone masking. The extent to which some of these phenomena can be correlated with, identified in, and predicted by the mechanical operation of the peripheral ear appears to be substantial.
TL;DR: A connecting network is an arrangement of switches and transmission links allowing a certain set of terminals to be connected together in various combinations, usually by disjoint chains (paths): e.g., a central office, toll center, or military communications system.
Abstract: A connecting network is an arrangement of switches and transmission links allowing a certain set of terminals to be connected together in various combinations, usually by disjoint chains (paths): e.g., a central office, toll center, or military communications system. Some of the basic combinatory properties of connecting networks are studied in the present paper. Three of these properties are defined informally as follows: A network is rearrangeable if, given any set of calls in progress and any pair of idle terminals, the calls can be reassigned new routes (if necessary) so as to make it possible to connect the idle pair. A state of a network is a blocking state if some pair of idle terminals cannot be connected. A network is nonblocking in the wide sense if by suitably choosing routes for new calls it is possible to avoid all the blocking states and still satisfy all demands for connection as they arise, without rearranging existing calls. Finally, a network is nonblocking in the strict sense if it has no blocking states. A distance between states can be defined as the number of calls one would have to add or remove to change one state into the other. This distance defines a topology on the set of states. Also, the states can be partially ordered by inclusion in a natural way. This partial ordering and its dual define two more topologies for the set of states. The three topologies so obtained are used to characterize (i.e., give necessary and sufficient conditions for the truth of) the three properties of rearrangeability, nonblocking in the wide sense, and nonblocking in the strict sense. Each of these three properties represents a degree of abundance of nonblocking states; the mathematical concept used to express these degrees is the topological notion of denseness.
TL;DR: Observations indicate that TASI is a more satisfactory method of increasing transatlantic cable capacity than alternate methods, such as the use of 2-kc channel banks.
Abstract: This article describes tests made to select design parameters for the speech detectors in the TASI system. Results of subjective tests carried out to determine maximum permissible loading of TASI circuits during busy hours are also described. Finally, conclusions drawn from observations on a working TASI system are given. These observations indicate that TASI is a more satisfactory method of increasing transatlantic cable capacity than alternate methods, such as the use of 2-kc channel banks.
TL;DR: In this paper, an iterative technique for simplifying Boolean functions is presented, which enables the user to obtain prime implicants by simple operations on a set of decimal numbers which describe the function.
Abstract: This article presents an iterative technique for simplifying Boolean functions. The method enables the user to obtain prime implicants by simple operations on a set of decimal numbers which describe the function. This technique may be used for functions of any number of variables.
TL;DR: In this paper, the problem of obtaining minimum-state sequential circuits for incompletely specified flow tables is addressed, where the only unspecified entries are those which occur because of restrictions on the allowed input-variable changes.
Abstract: This paper is concerned with the problem of obtaining minimum-state sequential circuits for incompletely specified flow tables Attention is directed to relay-type flow tables in which the only unspecified entries are those which occur because of restrictions on the allowed input-variable changes For this type of flow table it is shown that a simplified version of the Unger-Paull procedure is sufficient In particular, only maximum compatibles need be considered in forming the minimum-state sequential circuit
TL;DR: In this paper, an experimental 24-channel pulse code modulation system employing solid-state devices is described, and the authors present design considerations in meeting these requirements are presented in brief here and in detail in companion articles.
Abstract: An experimental 24-channel pulse code modulation system employing solid-state devices is described. Economy of design and ability to operate over existing exchange cable were dominant factors in selection of system organization and circuit alternatives. System requirements are unique to this type of system. Design considerations in meeting these requirements are presented in brief here and in detail in companion articles.
TL;DR: In this paper, a discussion of the phase-controlled loop with a sawtooth comparator is presented, where the main emphasis is on finding the pull-in range of the loop.
Abstract: Because of the recent interest in phase-controlled oscillators, a discussion of the phase-controlled loop with a sawtooth comparator is presented. The main emphasis is on finding the pull-in range of the loop. A companion paper in this issue (Ref. 4) deals with applications and shows how design parameters can be obtained from results developed here.
TL;DR: A computer simulation has been prepared which is capable of being applied to a large class of networks and several criteria are introduced and used to evaluate the relative performance of different networks, leading to conclusions regarding the merits of certain alternate routing procedures.
Abstract: As a first step in the investigation of communications networks with automatic alternate routing, a simulator has been prepared using the IBM 7090 high-speed digital computer. The simulator is capable of being applied to a large class of networks, the principal restrictions being that blocked calls are cleared, and no congestion or delay is encountered at the switching points. Although the first version of the simulation program requires that the alternate routing plan be fixed in advance (i.e., before a run), the program design is such that traffic-dependent alternate routing doctrines can easily be provided. The simulator has so far been used to examine the behavior of small networks of various sizes, configurations, and alternate routing doctrines under normal and abnormal conditions of load. Several criteria are introduced and used to evaluate the relative performance of different networks, leading to conclusions regarding the merits of certain alternate routing procedures and the areas of profitable application of the networks studied. The overload capabilities of these networks are of particular interest and are examined in some detail.
TL;DR: In this article, the problem of maintaining the most complex portion of an experimental electronic telephone switching system, the central control, was dealt with, where new and more effective automatic trouble detection and diagnostic techniques were used.
Abstract: This paper deals with the problem of maintaining the most complex portion of an experimental electronic telephone switching system, the central control. New and more effective automatic trouble detection and diagnostic techniques were used. In order to utilize these techniques effectively, a maintenance dictionary, i.e., a table relating trouble indications with corresponding faulty plug-in package, had to be produced. The system itself was utilized to create this dictionary. Over 50,000 known faults were purposely introduced into the central control to be diagnosed by its diagnostic program. The corresponding test results were then recorded via a high speed output. Finally, these test data were sorted and printed in dictionary form by a computer.
Journal Article•
[...]
TL;DR: In this paper, a more exact analysis is presented for the straight and curved waveguide and for all practical linings, in which the boundary value problem is formulated using wall impedances.
Abstract: The existing approximate analysis of wave propagation in lined waveguide is, under practical conditions, limited to linings thinner than 0.025 per cent of the waveguide diameter. A more exact analysis is presented here for the straight and curved waveguide and for all practical linings. In the case of anisotropic or sandwiched linings, the boundary value problem is formulated using wall impedances. The single isotropic lining is taken as an example to prove this formulation useful for typical cases. The exact analysis shows that neither the thickness nor the permittivity of the lining can increase the phase difference between TM 11 and TE 01 beyond a certain limit. The curvature coupling between these two waves is enhanced slightly by the lining.
TL;DR: In this paper, a digital computer is used to generate the 3D image of a given z = f (x, y) function and to wrap its surface with points of random brightness.
Abstract: Spatial models of functions of two variables are often a valuable research tool. Nomograms and artistic relief drawings in two dimensions are difficult to prepare and still lack the direct impact of a spatial object. It has been demonstrated (see Ref. 2) that objects with a randomly dotted surface permit the determination of binocular parallax and, thus, can be seen in depth even though they are devoid of all other depth cues. This random surface presentation has the advantage that the random brightness points can be evenly and densely placed, whereas the classical contour-line projection at equally spaced heights may leave empty spaces between adjacent contour-lines. A digital computer is used to generate the three-dimensional image of a given z = f (x, y) function and to wrap its surface with points of random brightness. The stereo projections of the function are obtained and, when viewed stereoscopically, give the impression of the three-dimensional object as being viewed along the z-axis. The random surface prevents the accumulation of clusters of uniform regions or periodic patterns which yield ambiguities when fused. Two stereo demonstrations are given of surfaces obtained by this method.