# Showing papers in "IEEE Transactions on Circuits and Systems in 1985"

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TL;DR: In this article, it was shown that any time-invariant continuous nonlinear operator with fading memory can be approximated by a Volterra series operator, and that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map.

Abstract: Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map. While previous approximation results are valid over finite time intervals and for signals in compact sets, the approximations presented here hold for all time and for signals in useful (noncompact) sets. The discretetime analog of the second theorem asserts that any TI operator with fading memory can be approximated (in our strong sense) by a nonlinear moving- average operator. Some further discussion of the notion of fading memory is given.

923Â citations

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TL;DR: In this paper, a detailed analysis of the geometric structure of a chaotic attractor observed from an extremely simple electrical circuit is given. And the chaotic nature of the attractor is further confirmed by calculating its associated Lyapunov exponents and Lyapeunov dimension.

Abstract: A detailed analysis is given of the geometric structure of a chaotic attractor observed from an extremely simple autonomous electrical circuit. It is third order, reciprocal, and has only one nonlinear element: a 3-segment piecewise-linear resistor. Extensive laboratory measurements from this circuit and a detailed geometrical analysis and computer simulation reveal the following rather intricate "anatomy" of the associated strange attractor. In addition to a microscopically infinite sheet-like composition the attractor has a macroscopic "double-scroll" structure, i.e., two sheetlike objects are curled up together into spiral forms with infinitely many rotations. (See frontispiece.) The chaotic nature of this circuit is further confirmed by calculating its associated Lyapunov exponents and Lyapunov dimension. The double-scroll attractor has one positive, one zero and one negative Lyapunov exponent. The Lyapunov dimension turns out to be a fractal between 2 and 3 which agrees with the observed structures. The power spectra of the three associated state variables obtained by both measurement and computer simulation show a continuous broad spectrum typical of chaotic systems.

602Â citations

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TL;DR: Explicit formulas for designing lattice wave digital filters of the most common filter types, for Butterworth, Chebyshev and Cauer parameter responses, were derived in this paper.

Abstract: Explicit formulas are derived for designing lattice wave digital filters of the most common filter types, for Butterworth, Chebyshev, inverse Chebyshev, and Cauer parameter (elliptic) filter responses. Using these formulas a direct top down design method is obtained and most of the practical design problems can be solved without special knowledge of filter synthesis methods. Since the formulas are simple enough also in the case of elliptic filters, the design process is sufficiently simple to serve as basis in the first part (filter design from specs to algorithm) of silicon compilers or applied to high level programmable digital signal processors.

259Â citations

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TL;DR: In this article, a new model for the study of transient stability where the load is modeled as a PQ bus is proposed, and an energy function is proposed which differs from the traditional one in that it includes additional terms corresponding to the energy stored in the loads and field winding.

Abstract: A new model is proposed for the study of transient stability where the load is modeled as a PQ bus. Flux decay of the generator field winding is included. The original network topology is maintained explicitly. An energy function is proposed which differs from the traditional one in that it includes additional terms corresponding to the energy stored in the loads and field winding. A characterization of the stability region is derived based on this energy function.

249Â citations

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TL;DR: In this article, simple algebraic methods may be used to design three-dimensional (3D) recursive digital filters for two important applications: first, the selective enhancement of a two-dimensional signal that is moving with time along a linear trajectory at known velocity.

Abstract: It is shown that simple algebraic methods may be used to design three-dimensional (3-D) recursive digital filters for two important applications: first, the selective enhancement of a two-dimensional (2-D) signal that is moving with time along a linear trajectory at known velocity and, second, the selective enhancement of 3-D spatially planar waves. The design techniques involve first-order 3-D networks in the continuous domain and proceed by analogy with an extension of the simple circuit theoretic concepts of resonance and Q factor. A 3-D spatial straight-line filter is designed in the frequency domain as a 3-D planar filter and, conversely, a 3-D spatially planar filter is designed in the frequency domain as a 3-D straight-line filter.

187Â citations

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TL;DR: In this paper, the design of voltage- or current-controllable linear transconductance elements needed for the continuous-time CMOS active filters is explored in detail, and circuit configurations, techniques of achieving linearity, and temperature compensation using the controlling variable are outlined.

Abstract: This paper explores in detail the possible approaches to. the design of voltage- or current-controllable linear transconductance elements needed for the design of continuous-time CMOS active filters. The focus of the paper is on circuit configurations, techniques of achieving linearity, and temperature compensation using the controlling variable. Circuit techniques for obtaining small transductance values are outlined. Simulation results are presented.

184Â citations

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TL;DR: In this paper, the minimum diameter, maximum connectivity circulant problem is considered and several results are given for the general case and a simple solution is derived for the connectivity four case.

Abstract: It is well known that maximum connectivity graphs play an important role in the design of reliable networks. The class of symmetric graphs called circulants is known to contain such maximum connectivity graphs. Although not all circulants have this maximum connectivity property, those that do have a great variation in their diameters. Since diameter is a measure of transmission delay, the minimum diameter, maximum connectivity circulant problem is considered here. Several results are given for the general case and a simple solution is derived for the connectivity four case.

116Â citations

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TL;DR: In this article, the lossless bounded-real lemma was developed in the discrete-time domain, based only on energy balance arguments, and the results were used to prove a discrete time version of the general Bounded-Real lemma, based on a matrix spectral factorization result that permits a transfer matrix embedding process.

Abstract: The Lossless Bounded-Real lemma is developed in the discrete-time domain, based only on energy balance arguments. The results are used to prove a discrete-time version of the general Bounded-Real lemma, based on a matrix spectral-factorization result that permits a transfer matrix embedding process. Some applications of the results in digital filter theory are finally outlined.

113Â citations

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TL;DR: In this paper, the authors developed, from certain basic assumptions, ultimate limits on dynamic range, chip area, and power consumption in SC integrators and low-pass filters, and showed that the minimum area and power requirements vary as the square of desired dynamic range.

Abstract: Switched-capacitor (SC) filters continue to improve in performance mainly through progress in the design of MOS operational amplifiers (op amps). Ultimate limits to achievable filter performance, however, stem from factors more fundamental than op amp nonidealities, factors independent of process and circuit improvements. This paper develops, from certain basic assumptions, ultimate limits on dynamic range, chip area, and power consumption in SC integrators and low-pass filters. For integrators, minimum area and power requirements are shown to vary as the square of desired dynamic range. Some physically realistic approximations lead to expressions relating filter area, power consumption, and dynamic range which involve only fundamental process parameters, supply voltage and filter cut-off frequency. Comparison with actual performance in typical commercially manufactured SC filters suggests that there is still a strong motivation in improving op amp specifications. A typical commercial fifth-order voiceband filter operating from a \pm 5-V supply with a dynamic range of 95 dB consumes approximately 5 mW and requires an area of approximately 5000 {mil}^{2} compared with the theoretical minima of 8.5 \mu W and 11.2 {mil}^{2} , respectively.

102Â citations

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TL;DR: In this paper, noniterative and iterative methods of system identification are applied to the determination of processor parameters in the noise canceler, and the computational requirements of each of the algorithms are compared.

Abstract: The computational complexity of nonlinear adaptive noise cancellation can be reduced by restricting the nonlinearity expected in the reference path to the noise canceler. The class of zero memory nonlinearities preceded by linear processors in the reference path is considered. Noniterative and iterative methods of system identification are applied to the determination of processor parameters in the noise canceler. The computational requirements of each of the algorithms are compared, and the iterative method is modified for improved convergence. Experimental results are presented for the modified iterative algorithm.

100Â citations

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TL;DR: In this paper, the applicability of the constructive stability algorithm of Brayton and Tong in the stability analysis of fixed-point digital filters is demonstrated. But the authors only consider direct and coupled digital filters and do not consider lattice filters.

Abstract: We demonstrate the applicability of the constructive stability algorithm of Brayton and Tong in the stability analysis of fixed-point digital filters. In the present paper, we consider direct form and coupled form filters while in a companion paper we treat wave digital filters and lattice filters. We compare our results with existing ones which deal with either the global asymptotic stability of digital filters or with existence (resp., nonexistence) of limit cycles in digital filters. Several of the present results are new while some of the present results constitute improvements over existing results. In a few cases, the present results are more conservative than existing results. It is emphasized that whereas the existing results are obtained by several diverse methods, the present results are determined by one unified approach.

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TL;DR: In this article, it was shown that for all these filters, filtering an arbitrary level signal is equivalent to decomposing the signal into binary signals, filtering each binary signal, and then reversing the decomposition.

Abstract: A useful class of robust nonlinear digital filters is the group of sliding window filters which use ranked order operations at each position of the window to produce the filter output. Median filters, alpha trimmed filters, and weighted rank filters are all included in this class. In this paper, it is shown that for all these filters, filtering an arbitrary level signal is equivalent to decomposing the signal into binary signals, filtering each binary signal, and then reversing the decomposition. This equivalence allows problems in the analysis and the implementation of these filters to be reduced to the equivalent problems for binary signals. Since the effects of ranked filters on binary signals are better understood, this technique is a powerful new tool.

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TL;DR: In this paper, simple closed-form bounds for signal propagation delay in linear RC tree models for MOS interconnects were derived, and these bounds are also valid for the more general class of linear networks known as RC meshes, which are useful as models for portions of MOS logic circuits that cannot be represented as RC trees.

Abstract: Simple closed-form bounds for signal propagation delay in linear RC tree models for MOS interconnect were derived in [1]. This paper shows that these bounds are also valid for the more general class of linear networks known as RC meshes, which are useful as models for portions of MOS logic circuits that cannot be represented as RC trees.

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TL;DR: In this paper, necessary and sufficient conditions are given for stability analysis of two-dimensional (2D) systems based on a Lyapunov approach using the Roesser state-space model.

Abstract: Some necessary and sufficient conditions are given for stability analysis of two-dimensional (2-D) systems based on a Lyapunov approach. The study was carried out using the Roesser state-space model, which when combined with the Lyapunov theory provides the new checkable tests for stability. Also, the results lead to techniques for selecting stabilizing state feedback gain matrices for the 2-D systems.

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TL;DR: In this article, the authors derived analytically the bifurcation diagram of the small amplitude ac forced Josephson junction and provided an enhanced picture of the dynamics of the ac forced case, as well as insightful explanation of the associated I-V characteristics.

Abstract: We study the dynamics of the Josephson junction circuit with both dc and ac current forcing, with emphasis on the ac case. Specifically, we derive analytically the bifurcation diagram of the small amplitude ac forced Josephson junction. We thus place on analytic grounds the qualitative, experimental, and simulation work of Belykh, Pedersen, and Soerensen; specially that which pertains to the regions of chaos. Combining previous results from the literature with our new results, we provide an enhanced picture of the dynamics of the ac forced case, as well as insightful explanation of the associated I-V characteristics. Explicit asymptotic formulae for the curves that separate the different regions in the bifurcation diagram are also given.

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TL;DR: The necessary and sufficient conditions for a digital filter transfer function to be implementable as a sum of two all-pass filters are derived directly in the z-plane as mentioned in this paper. But these conditions are not applicable to analog filters.

Abstract: The necessary and sufficient conditions are given for a digital filter transfer function to be implementable as a sum of two all-pass filters. The conditions are derived directly in the z -plane. The class of filters satisfying these conditions is shown to be wider than the class of filters obtained via the bilinear transformation from the corresponding conventional analog filters. An example shows that the given conditions enable us to design complementary filter pairs with different numerator and denominator orders directly using magnitude squared functions. These filters compare favorably with the corresponding classical filters.

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TL;DR: In this paper, a systematic method is given for generating negative-resistance circuits made of 2 transistors and linear positive resistors only, which can be integrated as a two-terminal device in monolithic form.

Abstract: A systematic method is given for generating negative-resistance circuits made of 2 transistors and linear positive resistors only. The 2 transistors may be bioolar ( n-p-n or p-n-p ), JFET ( n -channel or p-channel), MOSFET ( n -channel or p -channel), or their combinations. Since the circuits do not require an internal power supply, they are passive and can be integrated as a two-terminal device in monolithic form. Two algorithms are given for generating a negative-resistance device which exhibits either a type- N \upsilon - i characteristic similar to that of a tunnel diode, or a type- S \upsilon -i characteristic similar to that of a four-layered p-n-p-n diode. Hundreds of new and potentially useful negative resistance devices have been discovered. A selected catalog of many such prototype negative-resistance devices is included for future applications.

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TL;DR: In this article, the authors present a technique for signal synthesis in the presence of an inconsistent set of constraints, where the desired signal may be characterized as being an element of some Hilbert Space; each of the N design constraints generates a closed convex set in that space; and those convex sets generate, or may be resolved into, two disjoint closed sets, such that at least one of the two sets is bounded.

Abstract: In this paper, we present a novel technique for signal synthesis in the presence of an inconsistent set of constraints. This technique represents a general, minimum norm, solution to the class of synthesis problems in which: the desired signal may be characterized as being an element of some Hilbert Space; each of the N design constraints generates a closed convex set in that space; and those N convex sets generate, or may be resolved into, two disjoint closed convex sets, such that at least one of the two sets is bounded. The synthesis technique employs alternating nearest point maps onto closed convex subsets of a Hilbert Space, and may be viewed as an extension of D. Youla's "Method of Convex Projections"--which addresses the case in which the N closed convex sets, corresponding to the design constraints, possess a nonempty intersection. Section I provides a general introduction to the synthesis problem and to its solution. Section II contains the mathematical justification for the solution technique, while Section III presents an example of the synthesis of a data window for spectral estimation. In Section IV, we discuss potential extensions of this technique within the area of signal synthesis, as well as to the more general class of constrained optimization problems.

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TL;DR: In this paper, a criterion for the absence of zero-input limit cycles in state-space digital filters employing saturation arithmetic is presented, and an example is given, which brings out the novelity of the present approach.

Abstract: A criterion for the absence of zero-input limit cycles in state-space digital filters employing saturation arithmetic is presented. An example is given, which brings out the novelity of the present approach.

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TL;DR: In this article, the design of a finite-impulse-response digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the Steiglitz's program [1] is modified and then used to design a class of constrained FIR digital filters.

Abstract: The design of a (FIR) finite-impulse-response digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the Steiglitz's program [1] is modified and then used to design a class of constrained FIR digital filters. This class includes pulse shaping filters, N th band filters and nonuniform tap spacing filters, where some of the filter coefficients are constrained to zero. The advantage of the present approach, as compared to other methods, with regard to design speed and filter optimality and performance, are described, and illustrated by means of examples.

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TL;DR: In this article, the LBR-extraction approach is extended in order to derive wave digital filters and several orthogonal digital filters in a unified manner, which can therefore be implemented based on a simple building block, namely, the "planar rotation" operator.

Abstract: The LBR-extraction approach is extended in order to derive wave digital filters and several orthogonal digital filters in a unified manner. The derivation clearly places in evidence the underlying orthogonality property of all these structures, which can therefore be implemented based on a simple building block, namely, the "planar rotation" operator. The derivation directly emphasizes the concept of "structural boundedness" as a requirement for low sensitivity. In addition to wave and orthogonal filters, a number of other methods for forcing structural boundedness are indicated.

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TL;DR: This paper describes systolic realizations of FIR and IIR digital filters with sample rates much higher than the speed of a single "arithmetic unit" or "processing element" using a unitary or orthogonal similarity transformation.

Abstract: This paper describes systolic realizations of FIR and IIR digital filters with sample rates much higher than the speed of a single "arithmetic unit" or "processing element." The architecture trades increased throughput for increased latency. For IIR filters, the technique is based on block-state filter descriptions in which the state update matrix is converted to triangular or "quasi-triangular" form via a unitary or orthogonal similarity transformation. The effect of this transformation on the roundoff noise is examined in the Appendix. The latency, complexity, and suitability to VLSI implementations are considered, as well as an attractive application to interpolation and decimation.

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TL;DR: In this article, the authors report on some recent results in the mathematics of stochastic processes which suggest a mechanism leading to small disturbance instabilities of this type in power systems, and the assumptions necessary to structure the model to produce this behavior are simple, flexible and consistent with possible operating conditions in an electrical power system.

Abstract: Unstable, oscillatory behavior has been observed on several occasions in electrical power systems operated in an unfaulted, normal state under moderate load. In some cases system failure has resulted from this behavior. In this paper, we report on some recent results in the mathematics of stochastic processes which suggest a mechanism leading to small disturbance instabilities of this type in power systems. Unstable oscillations in power angles may be produced in a system consisting of a synchronous machine with negligible damping weakly coupled through randomly fluctuating links to other machines each with positive damping. The assumptions necessary to structure the model to produce this behavior are simple, flexible and consistent with possible operating conditions in an electrical power system.

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TL;DR: In this paper, the authors describe an algorithm for minimax design of two-dimensional FIR linear phase digital filters using a recently proposed minimax algorithm due to Charalambous in conjunction with Powell's conjugate direction algorithm to obtain the optimum results.

Abstract: In this paper we describe an algorithm for minimax design of two-dimensional FIR linear phase digital filters. A recently proposed minimax algorithm due to Charalambous in conjunction with Powell's conjugate direction algorithm will be used to obtain the optimum results. Optimal results obtained using the present approach on a large number of design examples are presented. Also a detail discussion on the effect of various symmetries of the impulse response on the amplitude response of the filter is presented.

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TL;DR: In this article, the authors presented finite impulse response switched-capacitor (SC) decimator and interpolator circuits based on nonrecursive polyphase structures, which are particularly suitable for narrow-band SC bandpass filter systems.

Abstract: This paper presents finite impulse response switched-capacitor (SC) decimator and interpolator circuits based on nonrecursive polyphase structures, which are particularly suitable for narrow-band SC bandpass filter systems. The circuits are attractive for integration and their good performance is demonstrated using practical discrete component models.

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TL;DR: In this paper a controller theory is introduced for multivariable 2-D systems together with stabilization algorithms based on state and output feedback techniques.

Abstract: In this paper a controller theory is introduced for multivariable 2-D systems together with stabilization algorithms based on state and output feedback techniques.

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TL;DR: In this paper, the authors extended the definition of the cross-Gramian matrix to include symmetric MIMO systems where the matrix W_{co} is defined as an integral.

Abstract: Recently, Laub et al. [1] and Fernando and Nicholson [2] extended the definition of the cross-Gramian matrix W_{co} to include symmetric MIMO systems where the matrix W_{co} is defined as an integral. In this correspondence, we define this matrix as a solution of a Lyapunov equation and prove the fundamental identity W_{co}^{2} = W_{c}W_{o} where W_{c} and W_{o} are the controllability and observability Gramians defined via Lyapunov equations. This definition of W_{co} complements the integral definition and has some advantages from theoretical and numerical points of view.

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TL;DR: In this article, a period-doubling route to chaos was reported from a laboratory model of the simplest possible chaotic autonomous circuit, which is made of two linear capacitors, one linear inductor, and only one nonlinear 2-terminal resistor.

Abstract: This paper reports a period-doubling route to chaos as observed from a laboratory model of the simplest possible chaotic autonomous circuit: it is made of two linear capacitors, one linear inductor, one linear resistor, and only one nonlinear 2-terminal resistor characterized by a 5-segment piecewise-linear \upsilon - i characteristic.

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TL;DR: In this article, a new technique is presented for the design of digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband.

Abstract: A new technique is presented for the design of digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband. The design is based entirely on an appropriate use of the well-known Remez-exchange algorithm for the design of weighted Chebyshev FIR filters. The extreme versatility of this algorithm is combined with certain "maximally flat" FIR filter building blocks, in order to generate a wide family of filters. The design technique directly leads to structures that have low passband sensitivity properties.