# Showing papers in "IEEE Transactions on Circuits and Systems in 1975"

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IBM

^{1}TL;DR: In this article, a modified nodal analysis (MNA) method is proposed, which retains the simplicity and other advantages of nodal Analysis while removing its limitations, and a simple and effective pivoting scheme is also given.

Abstract: The nodal method has been widely used for formulating circuit equations in computer-aided network analysis and design programs. However, several limitations exist in this method including the inability to process voltage sources and current-dependent circuit elements in a simple and efficient manner. A modified nodal analysis (MNA) method is proposed here which retains the simplicity and other advantages of nodal analysis while removing its limitations. A simple and effective pivoting scheme is also given. Numerical examples are used to compare the MNA method with the tableau method. Favorable results are observed for the MNA method in terms of the dimension, number of nonzeros, and fill-ins for comparable circuit matrices.

1,337 citations

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TL;DR: In this paper, a new algorithm is proposed for computing the transform of a band-limited function, which is a simple iteration involving only the fast Fourier transform (FFT), and it is shown that the effect of noise and the error due to aliasing can be controlled by early termination of the iteration.

Abstract: If only a segment of a function f (t) is given, then its Fourier spectrum F(\omega) is estimated either as the transform of the product of f(t) with a time-limited window w(t) , or by certain techniques based on various a priori assumptions. In the following, a new algorithm is proposed for computing the transform of a band-limited function. The algorithm is a simple iteration involving only the fast Fourier transform (FFT). The effect of noise and the error due to aliasing are determined and it is shown that they can be controlled by early termination of the iteration. The proposed method can also be used to extrapolate bandlimited functions.

1,034 citations

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Rice University

^{1}TL;DR: A unified approach to the analysis of periodically timevarying digital filters is introduced and it is shown that this method may be used to describe both time and frequency domain responses.

Abstract: A unified approach to the analysis of periodically timevarying digital filters is introduced. It is shown that this method may be used to describe both time and frequency domain responses. By considering multirate filters as a special class of periodically time-varying filters we have characterized the frequency response of a general multirate filter. A time domain synthesis procedure for periodically varying difference equations is also presented.

428 citations

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Bell Labs

^{1}TL;DR: In this paper, a new circuit simulator is described which combines the gate-to-gate signal propagation technique used in logic simulators with detailed device representation and circuit analysis at the gate level.

Abstract: A new circuit simulator is described which combines the gate-to-gate signal propagation technique used in logic simulators with detailed device representation and circuit analysis at the gate level. MOTIS is specialized for analyses of MOS logic circuits during the prelayout and postlayout phases of a design. The device modeling takes account of the back-gate bias effects and the bidirectionality of transmission gates. The simulation mechanism and the detailed device modeling lead to simulation of the dependence of propagation delays on input waveforms. The loading and device capacitances are assumed to be constant and bootstrapping effects are not simulated. The simulator has been implemented on a minicomputer having a 32K-word memory of 16-bit words, a disk module, and a storage CRT/keyboard terminal. This configuration allows simulation of circuits having 1000 gates with an operational speed of approximately 2 ms of real time per gate per nanosecond of circuit time.

286 citations

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TL;DR: In this paper, a class of low-sensitivity digital ladder filters may be realized in the voltage-current domain by direct analogy with the continuous resistively terminated LC ladder filter by using transformations that correspond to LC elements that exhibit finite Cube factors.

Abstract: A class of low-sensitivity digital ladder filters may be realized in the voltage-current domain by direct analogy with the continuous resistively terminated LC ladder filter The problem of unrealizability that is implied by delay-free loops in the discrete signal flow graph is overcome by using transformations that correspond to LC elements that exhibit finite Cube factors The resultant deterioration in the passband of the transfer function is determined from the Blowstein LC ladder sensitivity theory and is, thereby, shown to be low valued at high sampling frequencies The sensitivity properties of this class of digital ladder filters are directly analogous to the LC prototype because each LC element is replaced by a digital multiplier Consequently, if maximum power transfer is approximately maintained throughout the passband of the LC prototype, then the first-order sensitivity of the corresponding digital transfer function to multiply a coefficient quantization is necessarily low valued

200 citations

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TL;DR: For poles close to the unit circle and near z = 1, the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise as mentioned in this paper.

Abstract: For poles close to the unit circle and near z = 1 , the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise. As the sampling rate is increased the poles approach z = 1 and the problems become more severe. For these situations several new digital filter structures are presented for which the above errors remain constant and generally insignificant as the sampling rate is increased. Results on sensitivity and the roundoff errors for these new structures are presented and compared with conventional realizations. Some numerical results are also presented showing order of magnitude improvements.

161 citations

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TL;DR: In this article, it is shown that for wave digital filters, the earlier concept of pseudopower leads to a function called stored pseudo-power, from which a simple criterion guaranteeing absence of parasitic oscillations can be derived.

Abstract: Parasitic oscillations can occur in digital filters due to the granularity of the signal and to overflow. It is shown that for wave digital filters, the earlier concept of pseudopower leads to a function called stored pseudopower, from which a simple criterion guaranteeing absence of parasitic oscillations can be derived. For fixed-point two's-complement arithmetic, this criterion can be taken into account by particularly simple requirements for the adaptor output signals. A special type of calculus is developed which makes it possible to derive the corresponding simple requirements for the chopping operations at the various stages of the signal processing in the adaptors. The method is extended to cover scaling.

141 citations

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TL;DR: A new kind of circuit analysis program, EL, is presented, which employs heuristic "inspection" methods to solve rather complex dc bias circuits and has the ability to explain any result in terms of its own qualitative reasoning processes.

Abstract: A new kind of circuit analysis program, EL, is presented. Whereas other circuit analysis systems rely on classical, formal, analysis techniques, EL employs heuristic "inspection" methods to solve rather complex dc bias circuits. These techniques also give EL the ability to explain any result in terms of its own qualitative reasoning processes. EL's reasoning is based on the concept of a "local one-step deduction" augmented by various "teleological" principles and by the concept of a "macro-element." Several annotated examples of EL in operation and an explanation of how it works are presented. Also how EL can be extended in several directions, including sinusoidal steady-state analysis is shown. Finally, the possible implications of this work for engineering education and computer-aided design technology are discussed briefly. EL is significant not only as a novel approach to circuit analysis but also as an application of Artificial Intelligence techniques to a new and interesting domain.

104 citations

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TL;DR: In this article, recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in a finite number of steps, regardless of the degree of the polynomial.

Abstract: Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in a finite number of steps. Stability is tested with respect to either the half-plane or the unit circle applying only two times the equivalent of the Routh or Marden test, regardless of the degree of the polynomial.

97 citations

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Bell Labs

^{1}TL;DR: In this paper, a thin-film hybrid integrated circuit (HIC) is described, which is specifically manufactured to realize cascadable biquadratic active RC filter sections.

Abstract: This paper describes a thin-film hybrid integrated circuit (HIC) which is specifically manufactured to realize cascadable biquadratic active RC filter sections. The HIC consists of an RC network with one operational amplifier. This network is interconnected by a printed wiring board to realize Friend's Single Amplifier Biquad (SAB) and other filter sections. Design equations, components, predistortion method, and laser trimming are all discussed.

91 citations

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TL;DR: The Remez exchange algorithm is extended for the design of two-dimensional nonrecursive digital filters approximating circularly symmetrical low-pass specifications according to a weighted Chebyshev error norm.

Abstract: The Remez exchange algorithm is extended for the design of two-dimensional nonrecursive digital filters approximating circularly symmetrical low-pass specifications according to a weighted Chebyshev error norm. Since the approximating function does not satisfy the Haar condition, the optimal solution is not necessarily unique and a straightforward extension of the one-dimensional exchange method may fail to converge. It is shown how the algorithm has to be complemented with a perturbation technique in order to force convergence under all circumstances. In the case of nonuniqueness the solution provided by the algorithm is a vertex of the polyhedron containing all optimal solutions, and a method is given which allows one to compute an adjacent vertex located on the same edge, thereby allowing the successive determination of all the vertices defining the polyhedron. For this case also, a procedure is described which selects, among all optimal solutions, the best one according to some additional criterion. Finally, the efficiency and accuracy aspects of the algorithm are considered and practical conclusions are drawn as an aid for the designer.

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TL;DR: It is shown that by minimizing this statistical word length, the actual coefficient word length upon rounding of the coefficients can generally be reduced as well.

Abstract: A statistical approach is proposed for estimating the necessary coefficient word length of a digital filter. With this statistical word length definition, an optimization procedure is then proposed for minimizing the statistical word length for a given filter structure and a given set of maximum error constraints. It is shown that by minimizing this statistical word length, the actual coefficient word length upon rounding of the coefficients can generally be reduced as well. Several examples are given and improvements of one to three bits in the actual coefficient word length are observed. The procedure does not necessarily lead to the actual global minimum coefficient word length.

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TL;DR: In this paper, the authors derived algorithms for the realization of two-dimensional recursive digital filters using direct forms and continued fraction expansions, including a test for continued fraction expansion which at the same time determines the expansion coefficients.

Abstract: Algorithms are derived for realization of two-dimensional recursive digital filters using direct forms and continued fraction expansions. Included is a test for continued fraction expansion which at the same time determines the expansion coefficients. Transposed structures are also discussed, and a comparison is made of the various realizations.

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Bell Labs

^{1}TL;DR: In this article, the authors describe an algorithm for the identification of a minimal feedback vertex set of an arbitrary directed graph, such that removal of these vertices from the graph eliminates all directed loops.

Abstract: This paper describes an algorithm for the identification of a minimal feedback vertex set of an arbitrary directed graph. Such a set of vertices has the property that removal of these vertices from the graph eliminates all directed loops. An efficient solution to this identification problem is a familiar unsolved problem of contemporary graph theory. Although pathological examples exist for which excessive computation v2 time may be required, the described algorithm appears to be quite v efficient for large graphs arising in practical applications. The algorithm seems to have great potential in the field of test generation for sequential logic circuits and certain types of simulation algorithms. No attempt is V3 made to impose restrictive conditions on the particular minimum feedback vertex set selected, although such restrictions may at times be desirable. The algorithm has been implemented on an IBM 360/67 and has been successfully applied to practical (logic circuit) problems having in excess of 2500 vertices.

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TL;DR: In this article, a number of criteria are derived which give sufficient conditions for the absence of zero-input limit cycles in discrete-time and especially digital systems, and solutions to this problem for the case of a second-order digital filter with one and with two quantization nonlinearities are discussed.

Abstract: On the basis of a theorem of Barkin, a number of criteria are derived which give sufficient conditions for the absence of zero-input limit cycles in discrete-time and especially digital systems. These criteria are formulated in the frequency domain and provide a possibility of investigating the absence of a zero-input limit cycle of a specific length N . Depending on the particular characteristics of the nonlinearities and the number of nonlinearities in the system, different criteria are obtained. Application of the criteria results in most cases in a linear programming problem. The solutions to this problem for the case of a second-order digital filter with one and with two quantization nonlinearities are discussed.

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TL;DR: In this paper, a systematic search method was developed for obtaining the multiple solutions of a nonlinear equation of the form f(x) = 0, where f is a continuously differentiable function from R^n \rightarrrow R^N.

Abstract: A systematic search method has been developed for obtaining the multiple solutions of a nonlinear equation of the form f(x) = 0 , where f is a continuously differentiable function from R^n \rightarrrow R^n . The method is based on numerical integration of the associated system of differential equations \dot{f}_i = -f_i for i = 1, 2,\cdots , n - 1 and \dot{f}_n = \pm f_n along the space curve l of intersection f_i(x) = 0, i = 1, 2,\cdots, n - 1 . The plus or minus sign is chosen so as to make \{x_k\} move in the desired direction on l .

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TL;DR: A new gradient algorithm for the solution of nonlinear minimax problems has been developed and is well suited for automated minimax design of networks and it is very simple to use.

Abstract: A new gradient algorithm for the solution of nonlinear minimax problems has been developed. The algorithm is well suited for automated minimax design of networks and it is very simple to use. It compares favorably with recent minimax and least p th algorithms. General convergence problems related to minimax design of networks are discussed. Finally, minimax design of equalization networks for reflectiontype microwave amplifiers is carried out by means of the proposed algorithm.

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TL;DR: In this paper, a spatial clustering procedure applicable to multispectral image data is discussed, which takes into account the spatial distribution of the measurements as well as their distribution in measurement space.

Abstract: A spatial clustering procedure applicable to multispectral image data is discussed. The procedure takes into account the spatial distribution of the measurements as well as their distribution in measurement space. The procedure calls for the generation and then thresholding of the gradient image, cleaning the thresholded image, labeling the connected regions in the cleaned image, and clustering the labeled regions. An experiment was carried out on ERTS data in order to study the effect of the selection of the gradient image, the threshold, and the cleaning process. Three gradients, three gradient thresholds, and two cleaning parameters yielded 18 gradient-thresholds combinations. The combination that yielded connected homogeneous regions with the smallest variance was Robert's gradient with distance 2, thresholded by its running mean, and a cleaning process that considered a resolution cell to be homogeneous if and only if at least 7 of its nearest neighbors were homogeneous.

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Philips

^{1}TL;DR: In this article, the forced response of a general type of digital filter, implemented with overflow nonlinearities, is studied, and a definition of stability of this forced response is given.

Abstract: The forced response of a general type of digital filter, implemented with overflow nonlinearities, is studied. A definition of stability of this forced response is given. It is indicated that this stability can be studied by means of the zero-input behavior of a system, with the same structure but with time-varying nonlinearities. A theorem is derived giving sufficient conditions for the stability of the forced response of a digital system. Some results of the application of this theorem to wave digital filters are given.

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TL;DR: In this article, a new recursive procedure based on state-space techniques and the use of a Kalman-Bucy filter is presented to solve the restoration problem of images degraded by motion in one direction.

Abstract: A new recursive procedure, based on state-space techniques and the use of a Kalman-Bucy filter is presented to solve the restoration problem of images degraded by motion in one direction. Both the noisefree and the noisy cases are considered.

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TL;DR: In this paper, a solution to the identification problem for a class of nonlinear systems, based on steady-state frequency response, is presented, which is composed of certain interconnections of stable linear dynamic systems and integer power nonlinearities.

Abstract: A solution to the identification problem for a class of nonlinear systems, based on steady-state frequency response, is presented. This class is composed of certain interconnections of stable linear dynamic systems and integer power nonlinearities. Two kinds of measurements are considered. The first involves obtaining the amplitude and relative phase of each harmonic of the steady-state frequency response, while the second involves measuring the amplitudes only. In each case we find the number of measurements sufficient to identify a system for which the highest power present and the bounds on the dimensions of the linear subsystems are known.

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TL;DR: In this paper, the problem of finding disjoint dominating sets in a graph is studied, in particular, the domatic number d(G) of a graph G is defined as the maximum order of a partition of the vertices of G into dominating sets.

Abstract: Graph theoretic techniques provide a convenient tool for the investigation of communication networks. Here a communication network is represented by a nonoriented linear graph, in which the edges represent communication links and the vertices represent cities. A transmitting group is a set of cities which, acting as transmitting stations, can transmit messages to every city in the network. Stated graph theoretically, a transmitting group is a dominating set, i.e., a set of vertices D having the property that any vertex not in D is adjacent to at least one vertex in D . The problem of finding disjoint dominating sets in a graph is studied, in particular, the domatic number d(G) of a graph G is defined as the maximum order of a partition of the vertices of G into dominating sets.

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TL;DR: A nonlinear method of estimating pictorial data from noisy observations is considered and an edge detection technique using likelihood functions is used to decide if an incoming picture element is a member of the object or the background.

Abstract: A nonlinear method of estimating pictorial data from noisy observations is considered. The data is assumed to be composed of an object with one texture in the background. An edge detection technique using likelihood functions is used to decide if an incoming picture element is a member of the object or the background. Then, the picture element is directed to one of the two Kalman filters designed based upon the statistics of the object or the background accordingly.

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TL;DR: In this paper, the frequency weighted least-square design of finiteduration filters, in one and two dimensions, continuous and discrete, is considered and some new theoretical results and some practical design techniques for conventional and unconventional filters are presented.

Abstract: The frequency weighted least-square design of finiteduration filters, in one and two dimensions, continuous and discrete is considered. Some new theoretical results and some practical design techniques for conventional and unconventional filters are presented. In some cases optimum discrete filters can be found conveniently by matrix inversion. In many cases a simple, iterative approximation technique using FFT can be used to carry out the design or to adjust the frequency response of filters.

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TL;DR: In this article, a comparative study of single-amplifier filters, fifteen different two-AMplifier circuits, and the state-variable three-AMPLIFIER configuration is given.

Abstract: A comparative study of single-amplifier filters, fifteen different two-amplifier circuits, and the state-variable three-amplifier configuration is given. The figures-of-merit used are the passive sensitivities, the \omega_0 gain-sensitivity products, the Q gain-sensitivity products, and the \omega_0 and Q deviations due to the amplifiers' limited bandwidth. In addition, practical matters such as input impedance and component spread are considered. Among the circuits considered a particular twoamplifier resonator emerges as the "best" biquadratic section. Some of the interesting results include a unified expression, applicable to a large class of low-sensitivity circuits, for the \omega_0 deviation due to the amplifier's limited frequency response. In this expression, which applies for all active filters which have low \omega_0 active sensitivities, the only configurationdependent quantities are the Q gain-sensitivity products.

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TL;DR: In this paper, a method for the synthesis of active filters based on processing of wave quantities is presented and some experimental results confirm the feasibility of the principle and possibilities for practical implementation are shown.

Abstract: Inductorless active filters which are derived from double terminated classical reactance filters, such as gyrator-capacitor filters and filters using the FDNR concept, are known to exhibit low sensitivity. Stimulated by the ideas underlying the method of wave digital filters the attempt has been made to establish a concept for the synthesis of active filters which is based on processing of wave quantities. In this paper the method leading to this new kind of active filters is presented and possibilities for practical implementation are shown. Some experimental results confirm the feasibility of the principle.

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TL;DR: In this paper, a broadbanding theory for high-frequency transistor amplifiers is presented, where the transistor is modeled as a reactively constrained active two-port network, and a class of practical broad-band matching networks are considered.

Abstract: The design of broad-band high-frequency transistor amplifiers is a difficult and challenging outstanding problem in active network theory of great practical importance. New and explicit optimum gain-bandwidth limitations of high-frequency transistor amplifiers for arbitrary prescribed transistor gain rolloff characteristics are presented. The transistor is modeled as a reactively constrained active two-port network. The limitations derived and presented are applicable to the design of broad-band small-signal as well as high-power transistor amplifiers. Realization of a class of practical broad-band matching networks are also presented. The explicit gain-bandwidth limitations and the new realization results presented form the basis for a new broadbanding theory for high-frequency transistor amplifiers and represent a significant advancement in the design theory of active networks.

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TL;DR: An algorithm is presented for solving nonlinear ordinary differential equations that generates a broad class of implicit linear differentiation formulas that is more efficient as to the number of arithmetic operations than Brayton's algorithm, as well as more general and systematic.

Abstract: An algorithm is presented for solving nonlinear ordinary differential equations that generates a broad class of implicit linear differentiation formulas. Specific interest is concerned in one type of formula which for constant timestep reduces to the well-known Gear formulas. Although these formulas are mathematically fully equivalent to the BDF formulas as presented by Brayton et al. [1], their construction is quite different. Instead of using previously calculated function values, we employ predictions extrapolated from these values to set up and evaluate the differentiation formula. A recursive relation for these predictions is derived in order to simplify their calculation in the next timestep. As predictions are needed for order and error control, our algorithm appears to be more efficient as to the number of arithmetic operations than Brayton's algorithm, as well as more general and systematic. Moreover, a change of the order can be accomplished without extra work. Due to the available predictions, an interpolation to determine function values at intermediate time instants, as for instance required in plotting procedures, can be performed in a fast way.

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TL;DR: In this article, an active filter with resistors and two operational amplifiers represented by their single-pole model, but no external capacitors, is discussed, which is suitable for high-frequency and medium-Q applications.

Abstract: An active filter is discussed which uses only resistors and two operational amplifiers represented by their single-pole model, but no external capacitors. The filter has very low sensitivities to all circuit parameters, is tunable over exceptionally wide frequency ranges, and is suitable for high-frequency and medium- Q applications. The usable frequency range is limited only by the validity of the single-pole model of the amplifiers used. The circuit may be used both as a lowpass and as a bandpass. Extensive room-temperature experimental results are presented.

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TL;DR: The main part of this paper describes how to create efficiently a data structure which allows the use of approximation techniques to obtain consistent polygonal outlines of the objects in a picture.

Abstract: The main part of this paper describes how to create efficiently a data structure which allows the use of approximation techniques to obtain consistent polygonal outlines of the objects in a picture. In addition, it gives a method for editing the regions obtained from the application of a segmentation algorithm. Examples involving solid geometrical objects, X-ray pictures, and human faces are given.