Scheduled System Maintenance:
Some services will be unavailable Sunday, March 29th through Monday, March 30th. We apologize for the inconvenience.
By Topic

Circuit Theory, IRE Transactions on

Issue 4 • Date December 1956

Filter Results

Displaying Results 1 - 21 of 21
  • Systems Analysis of Discrete Markov Processes

    Publication Year: 1956 , Page(s): 257 - 266
    Cited by:  Papers (32)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1161 KB)  

    The properties of discrete Markov processes are related to those of analogous linear, time-invariant, sampled-data systems. Methods are given for the systems-analysis solution and interpretation of problems and theorems relating to such Markov processes. Correlation functions of signals generated by Markov processes are determined. Transform procedures, flow graphs, and signal-flow ideas play an important role in these studies. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the chain matrix of cascaded networks

    Publication Year: 1956 , Page(s): 297 - 298
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (222 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Abstracts of Foreign Language Articles on Circuit Theory

    Publication Year: 1956 , Page(s): 297
    Save to Project icon | Request Permissions | PDF file iconPDF (120 KB)  
    Freely Available from IEEE
  • Prospectus for IRE Transactions on Active Networks

    Publication Year: 1956 , Page(s): 298 - 299
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (265 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Ladder Network Analysis by Signal-Flow Graph-Application to Analog Computer Programming

    Publication Year: 1956 , Page(s): 289 - 294
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (552 KB)  

    S. Mason's signal flow graph technique is applied to the analysis of ladder networks. Briefly, the flow graph of a ladder is developed using Ohm's and the two Kirchhoff's equations. The graph is then reciprocated so that it contains only forward paths. The transfer function, in the case of a simple ladder, is the reciprocal of the sum of all distinct paths from the output to the input node. In the case of ladders containing internal generators, independent or dependent, the transfer function can be found in a similar way with slight modifications. Other relations, such as the input impedance, transfer admittance, etc., can also be found directly from the flow graph. In essence, instead of writing mesh equations or applying recursion formulas of continuants, we construct a flow graph by inspection and analyze the network from the graph. In the last part of the paper, the striking similarities between the flow graph of a network and its analog computer simulation are pointed out. Indeed, the flow graph is the computer set-up in a schematic form. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Limiting Conditions on the Correlation Properties of Random Signals

    Publication Year: 1956 , Page(s): 299
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (176 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Inter-Reciprocity Applied to Electrical Networks

    Publication Year: 1956 , Page(s): 296 - 297
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The Continuous Delay-Line Synthesizer as a System Analogue

    Publication Year: 1956 , Page(s): 295 - 296
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (280 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The Use of Least Squares in System Design

    Publication Year: 1956 , Page(s): 224 - 231
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1008 KB)  

    Approximation, realization, and alignment in the circuit theoretic sense are the essential ingredients in the development of a large class of physical systems. It is shown that the method of least squares is an effective tool for obtaining "optimum" performance in the three facets of system design. Tangent descent and Taylor Series are recommended for use in the application of least squares to system design. The mathematical processes inherent in this procedure have been programmed for solution by a digital computer. The marriage of digital computers to this means of system design has been compatible, and "offsprings" are displayed to attest to this fact. These examples include: 1) alignment of a one port to match a prescribed magnitude characteristic, and 2) synthesis of all-pass networks into a composite delay equalizer. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the Identification Problem

    Publication Year: 1956 , Page(s): 277 - 281
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (568 KB)  

    The identification problem involves the determination of the identity of a black box from the observation of its responses to a set of input signals. In this paper attention is focused on the identification of zero-memory multipoles and two-poles of class n_1 . The test signals are sine waves of different amplitudes and frequencies, and the measured quanity is the describing function of the device. In the case of two-poles of class n_1 , it is found that the describing function is related to the characteristic function by an integral equation of second order which can be solved explicitly by the use of the Fourier-Hankel transformation. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Definitions of 'Bandwidth' and 'Time Duration' of Signals Which Are Connected by an Identity

    Publication Year: 1956 , Page(s): 286 - 288
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (264 KB)  

    In this paper we give definitions of "equivalent time duration" \Delta \tau and "equivalent bandwidth" \Delta f and show that they are connected by a simple reciprocal identity. An example is given and it is shown that the same concepts can be applied in antenna theory to give useful definitions of "equivalent aperture distribution width" and "equivalent angular spectrum." View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On Nonuniform Sampling of Bandwidth-Limited Signals

    Publication Year: 1956 , Page(s): 251 - 257
    Cited by:  Papers (156)  |  Patents (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (824 KB)  

    The purpose of this investigation is to examine four special nonuniform sampling processes in detail, and to deduce some interesting properties of bandwidth-limited signals. The main results are contained in four generalized sampling theorems. These theorems not only contain the nature of determination (unique-specification, over-specification, and underspecification) of signals but also include explicit reconstruction formulas. From the reconstruction formulas, the complexity and accuracy of the nonuniform sampling processes discussed can be estimated. In addition, these theorems lead to observations regarding the allowable shapes, the "prediction," and the "energy" of bandwidth-limited signals in general. A "minimum-energy" signal is introduced which has certain advantages as compared to the ordinary "time-limited" signals when a finite number of sample values are given. Finally, a statement due to Cauchy on the sampling of bandwidth-limited signals is generalized to include a wider class of nonuniform sample point distributions and modified to give more exact information regarding the nature of determination of signals. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • System Theory as an Extension of Curcuit Theory

    Publication Year: 1956 , Page(s): 217 - 223
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (992 KB)  

    The attitudes and techniques of circuit analysis and synthesis can profitably be extended to system analysis and design. The main problems of system analysis are characterization of components and combination of component characteristics into system characteristics. Techniques analogous to familiar circuit theory techniques are applicable to the study of noncircuit problems. As an example, the analysis of a discrete-data system is described. Such familiar network theory terms as transfer function, transform, stability, return difference, and error coefficients are used. Applications of system analysis techniques to the study of convergence of iterative methods for solving equations and to the study of error propagation are described. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A Transistorized DC Amplifier

    Publication Year: 1956 , Page(s): 285
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (92 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Limiting Conditions on the Correlation Properties of Random Signals

    Publication Year: 1956 , Page(s): 282 - 285
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (464 KB)  

    A system of n signals that has random character is completely characterized by its self-power spectra and cross-power spectra which, when normalized, can be combined in a correlation matrix. It is shown that the correlation matrix must fulfill the fundamental condition that none of its principal minors is negative. It is shown that no further restriction exists, that is, that all correlation matrices fulfilling this condition are realizable. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Signal Theory

    Publication Year: 1956 , Page(s): 210 - 216
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (968 KB)  

    It is suggested that much of the subject matter now lumped under the heading of "circuit theory" might better be called "system theory," which in turn may be separated into three subdivisions-that which deals with the representation of the physical elements; that which deals with the representation of the signals, and that which deals with the representation of the transformations and relations between the signals and the elements. For the first subdivision, the name "circuit theory" in its original sense is suggested; for the second subdivision, the name "signal theory;" and for the third, the name "operator theory." This paper describes some of the distinctions between the first and second subdivisions. Signal representations are needed for two purposes: To study the transmission properties of a system, and to reveal the information-bearing attributes of a signal. Steady-state (i.e., Fourier) representations are well suited to the first purpose, but representations that explicitly involve temporal parameters are needed for the latter purpose. The expansions of signals in terms of nonsinusoidal components provide one type of representation which has been used extensively in physics but has been little used in the practical analysis of signals. A specific example is given of a filter structure which analyzes the incoming signal in terms of a set of orthogonal functions formed from the exponential components e^{-t}, e^{-2t}, e^{-3t} , etc., and it is shown how an "ideal" filter, in the sense of Zadeh, may be constructed for separating these components. A practical use of this ideal filter is to measure the nonlinear distortion of an arbitrary dynamical system under transient conditions. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A Study of Rough Amplitude Quantization by Means of Nyquist Sampling Theory

    Publication Year: 1956 , Page(s): 266 - 276
    Cited by:  Papers (87)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1288 KB)  

    Quantization is an operation that takes place when a physical quantity is represented numerically. It is the assignment of an integral value to a physical quantity corresponding to the nearest number of units contained in it. Quantization is like "sampling-in-amplitude," which should be distinguished from the usual "sampling-in-time." The probability density distribution of the signal is sampled in this case, rather than the signal itself. Quantized signals take on only discrete levels and have probability densities consisting of uniformly-spaced impulses. If the quantization is fine enough so that a Nyquist-sampling restriction upon the probability density is satisfied, statistics are recoverable from the grouped statistics in a way similar to the recovery of a signal from its samples. When statistics are recoverable, the nature of quantization "noise" is understood. As a matter of fact, it is known to be uniformly distributed between plus and minus half a unit, and it is entirely random (first order) even though the signal may be of a higher-order process, provided that a multidimensional Nyquist restriction on the high-order distribution density is satisfied. This simple picture of quantization noise permits an understanding of round-off error and its propagation in numerical solution, and of the effects of analog-to-digital conversion in closed-loop control systems. Application is possible when the grain size is almost two standard deviations. Here the dynamic range of a variable covers about three quantization boxes. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Analysis of Linear n-Port Networks

    Publication Year: 1956 , Page(s): 296
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (168 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A System-Theory Perspective for Signal Theory

    Publication Year: 1956 , Page(s): 208 - 209
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (264 KB)  

    First Page of the Article
    View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Signal Theory in Speech Transmission

    Publication Year: 1956 , Page(s): 232 - 244
    Cited by:  Papers (7)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1680 KB)  

    The mechanism of speech production imposes a number of well-defined constraints on the resulting acoustic wave. The nature of these constraints is associated with the anatomy of the human vocal tract and vocal cords. This mechanism can be characterized as a time-varying linear dynamic system excited alternatively by a noise or pulse source which contains only frequencies much higher than the variational rate. Thus, speech can be described by a small number of parameters which change at the slower rate. Such parameters in effect describe the constants of the dynamic system and its excitation. Representations of this kind demonstrate the philosophy underlying the signal theory approach to the design and analysis of transmission circuits. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The Theory of Analytic Band-Limited Signals Applied to Carrier Systems

    Publication Year: 1956 , Page(s): 244 - 251
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (952 KB)  

    The recently-developed concept of the "analytic signal," together with that of bandwidth-limited signals, is used to construct a general theory of amplitude modulation. The basic definition and properties of an "analytic signal" are reviewed with particular reference to band-limited signals. The "analytic signal" is a signal of the form z(t) = x(t) + jy(t) = p(t)e^{j\varphi (t)} where x(t) and y(t) have the same norms, are orthogonal and related to one another by the Hilbert transform, and where p(t) = \sqrt {x^{2}+y^{2}} defines an envelope function while \varphi (t) = \tan^{-1}y(t)/x(t) defines a phase function whose rate of change determines an instantaneous frequency. The Fourier transform Z(\omega ) for z(t) is identically zero for \omega < 0 . The theory of amplitude modulation based on the band-limited analytic signal is used to define clearly the properties of single-sideband transmission systems. The problem of amplifier overloading in multiplex single-sideband transmission is referred to and some comparisons are drawn between the amplitude probability distributions of the envelopes of double and single-sideband transmission of random signals. It is suggested that the concept of the analytic bandwidth-limited signal may facilitate the development of a general theory of frequency modulation. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.