Showing papers in "IEEE Transactions on Circuits and Systems in 1978"
TL;DR: In this article, a review of the algebras related to Kronecker products is presented, which have several applications in system theory including the analysis of stochastic steady state.
Abstract: The paper begins with a review of the algebras related to Kronecker products. These algebras have several applications in system theory including the analysis of stochastic steady state. The calculus of matrix valued functions of matrices is reviewed in the second part of the paper. This calculus is then used to develop an interesting new method for the identifiication of parameters of lnear time-invariant system models.
1,944 citations
TL;DR: In this article, the authors adopt a view that many problems of image restoration are probably geometric in character and admit the following initial linear formulation: the original f is a vector known a priori to belong to a linear subspace of a parent Hilbert space, but all that is available to the observer is its image P_{a} f, the projection of f onto a known linear sub space, also in \cal H ).
Abstract: We adopt a view that suggests that many problems of image restoration are probably geometric in character and admit the following initial linear formulation: The original f is a vector known a priori to belong to a linear subspace {\cal P}_b of a parent Hilbert space {\cal H}( , but all that is available to the observer is its image P_{a} f , the projection of f onto a known linear subspace {\cal P}_a (also in \cal H ). 1) Find necessary and sufficient conditions under which f is uniquely determined by P_{a} f and 2) find necessary and sufficient conditions for the stable linear reconstruction of f from P_{a} f in the face of noise. (In the later case, the reconstruction problem is said to be completely posed.) The answers torn out to be remarkably simple. a) f is uniquely determined by {\cal P}_{a} iff {\cal P}_{b} and the orthogonal complement of { \cal P}_{a} have only the zero vector in common. b) The reconstruction problem is completely posed iff the angle between {\cal P}_{b} and the orthogonal complement of {\cal P}_{a} , is greater than zero. (All angles lie in the first quadrant.) c) In the absence of noise, there exists in both cases a) and b) an effective recursive algorithm for the recovery of f employing only the operations of projection onto {\cal P}_{b} and projection onto the orthogonal complement of {\cal P}_{a} These operations define the necessary instrumentation.
372 citations
TL;DR: In this paper, a natural matrix extension of the classical theory of orthogonal polynomials on the unit circle introduced by Szego is proposed, which is a unifying concept in various mathematical aspects of circuit and system theory.
Abstract: This paper proposes a natural matrix extension of the classical theory of orthogonal polynomials on the unit circle introduced by Szego. As a result, orthogonal polynomial matrices appear to be a unifying concept in various mathematical aspects of circuit and system theory.
237 citations
TL;DR: In this article, a quotient algebra of transfer functions of distributed linear time-invariant subsystems is proposed; this algebra is a generalization of the algebra of proper rational functions.
Abstract: A quotient algebra of transfer functions of distributed linear time-invariant subsystems is proposed; this algebra is a generalization of the algebra of proper rational functions. Its main virtue is that it allows the algebraic manipulation of distributed systems within the algebra. Series, parallel, and, under some regularity conditions, feedback interconnection of transfer functions in the algebra remain in the algebra. The relation of our algebra to the algebras proposed by Morse, Dewilde, and Kamen is discussed and the algebras are compared. Finally, applications of the algebra are indicated.
225 citations
TL;DR: In this paper, the authors describe design techniques for monolithic, high-precision, MOS sampled-data active-ladder filters, which are used to simulate doubly terminated LC ladder networks.
Abstract: Design techniques for monolithic, high-precision, MOS sampled-data active-ladder filters are described. Switched capacitor integrators are used to implement the "leapfrog" configuration for simulating doubly terminated LC ladder networks. Techniques are presented for designing all-pole low-pass filters, as well as methods for including transmission zeros. An approach for implementing bandpass filters is described which is derived from the conventional low-pass-to-bandpass transformation. Monolithic realizations for two different low-pass filters are briefly described which show excellent agreement with theory.
217 citations
TL;DR: The design of Nth-order oversampled coders and an experimental third-order predictive coder are described, allowing N+1/2 bits to be eliminated from the coder's A/D for each doubling of the sample rate.
Abstract: First-order predictive coders (e.g., DPCM) and first-order noise shaping coders (e.g, interpolative coders) are familiar A/D conversion techniques. Using a feedback network containing an A/D and a first-order (single-pole) analog filter, they reduce the number of A/D output levels, for a given SNR requirement, at the expense of the additional analog filter complexity. Oversampling (i.e., sampling at higher than the Nyquist rate) provides excess bandwidth in the feedback loop, allowing further reductions in the number of A/D output levels at the expense of faster circuitry. This paper extends such first-order oversampled coders to include higher order analog filters under the constraint that the filters be independent of the statistical properties of the input analog signal. The resulting robust Nth-order predictive and noise-shaping coders allow N+1/2 bits to be eliminated from the coder's A/D for each doubling of the sample rate. The design of such Nth-order oversampled coders and an experimental third-order predictive coder are described.
193 citations
TL;DR: In this article, it was shown that a technique due to Bauer for the Wiener-Hopf factorization of scalar polynomials that are nonnegative on the unit circle, can be extended to arbitrary integrable periodic n \times n nonnegative-definite Hermitian matrices K(\theta) which satisfy the Paley-Wiener criterion.
Abstract: In this paper it is shown that a technique due to Bauer for the Wiener-Hopf factorization of scalar polynomials that are nonnegative on the unit circle, can be extended to arbitrary integrable periodic n \times n nonnegative-definite Hermitian matrices K(\theta) which satisfy the Paley-Wiener criterion. This is the most general possible setting. The resulting algorithm agrees with the one derived recently by Rissanen and Kailath but is established in an elementary manner without the imposition of any unnecessary constraints. The method also supplies some detailed information regarding the nature of the convergence. An important byproduct of the analysis is the clarification of the role played in spectral factorization by two sets of matrix orthogonal polynomials generated by the weight K(\theta) . These polynomials can be generated recursively and a study of their limiting properties reveals that they provide an effective alternative scheme for the construction of the desired Wiener-Hopf factor. Since the matrix K(\theta) is not restricted to be the boundary value of some rational matrix, the algorithm can also be employed in the solution of many different types of electromagnetic field problems centered around the Wiener-Hopf idea.
167 citations
TL;DR: In this paper, the authors show the correspondence between the Darlington synthesis procedure, well known in the network theory literature, J -coprime (MFD) representations of transfer functions, the Szego-Levinson theory of orthogonal polynomials on the unit circle, and the theory of generalized Schur indices.
Abstract: We show the correspondence between the following: i) the Darlington synthesis procedure, well known in the network theory literature; ii) J -coprime (MFD) representations of transfer functions; iii) the Szego-Levinson theory of orthogonal polynomials on the unit circle; iv) the theory of generalized Schur indices; and v) the theory of NevanlinnaPick approximations. More specifically: i) and ii) are equivalent, ii) and iv) are also equivalent for a subclass of i) and ii), while v) provides a nice framework for the study of convergence properties. The paper produces also an exact and an approximate construction procedure of prediction and modeling filters of a general (ARMA) type, for stationary processes, and shows its convergence.
159 citations
TL;DR: The results of an investigation of the structure and stability of various oscillatory modes of an inductance coupled ring of the van der Pol oscillators, using a nonlinear mode analysis, are presented in this article.
Abstract: The results of an investigation of the structure and stability of various oscillatory modes of an inductance coupled ring of the van der Pol oscillators, using a nonlinear mode analysis, are presented. It has been demonstrated that all single modes, both standing and traveling waves, are stable, but that simultaneous two and three modes are not stable. Experiments have been performed using four- and five-oscillator rings and the results obtained agree well with the theory.
154 citations
Abstract: Quantization is the process of replacing analog samples with approximate values taken from a finite set of allowed values. The approximate values corresponding to a sequence of analog samples can then be specified by a digital signal for transmission, storage, or other digital processing. In this expository paper, the basic ideas of uniform quantization, companding, robustness to input power level, and optimal quantization are reviewed and explained. The performance of various schemes are compared using the ratio of signal power to mean-square quantizing noise as a criterion. Entropy coding and the ultimate theoretical bound on block quantizer performance are also compared with the simpler zero-memory quantizer.
153 citations
TL;DR: In this article, it was shown that if certain natural conditions are satisfied S possesses an equilibrium point, and if additional reasonable conditions are met the equilibrium point is unique and globally stable.
Abstract: The basic equations of compartmental analysis are a system S of differential equations which govern the exchanges of material among various compartuments and an environment. The equations are ordinarily nonlinear. In this paper we show that if certain natural conditions are satisfied S possesses an equilibrium point, and that if additional reasonable conditions are met the equilibrium point is unique and globally stable. These results have natural interpretations and, in particular, provide an analytical basis for the use of the familiar linear tracer-analysis equations. We also consider the case in which S takes into account cyclic variations with a given period \tau (this case often arises in ecological studies) and show that under certain reasonable conditions S has a \tau -periodic solution that is approached by every solution of S.
TL;DR: An analytical representation for m -dimensional piecewise-linear functions which are affine over convex polyhedral regions bounded by linear partitions is introduced in this paper, where explicit formulas are presented to compute the coefficients associated with this representation along with an example.
Abstract: An analytical representation is introduced for m -dimensional piecewise-linear functions which are affine over convex polyhedral regions bounded by linear partitions. Explicit formulas are presented to compute the coefficients associated with this representation along with an example.
TL;DR: In this article, the stability properties of a class of nonlinear compartmental systems are discussed. But the authors do not consider the nonoscillatory properties of solutions and show that the system has no periodic oscillation under a mild condition, and a sufficient condition for the origin to be globally asymptotically stable.
Abstract: This paper discusses properties related to the stability of a class of nonlinear compartmental systems. Specifically, mathematical conditions which guarantee the same qualitative behavior inherent in linear compartmental systems are considered. We first consider the nonoscillatory property of solutions and show that the system has no periodic oscillation under a mild condition. The result is then used to derive a necessary and sufficient condition for every solution to converge to a set of equlibrium points which may depend both on the input and the initial state. A sufficient condition is also given for an equilibrium state to depend only on the input. The asymptotic behavior of the free systems is also considered, and a sufficient condition is given for the origin to be globally asymptotically stable. Furthermore, for a closed compartmental system it is shown that for each given initial state, unique equilibrium state, if it exists, depends only on the total sum of the components of the initial state. Finally a sufficient condition is given for solutions to converge to the unique point.
TL;DR: A fast band-limited signal extrapolation technique is presented where the total extrapolation process is achieved by a single matrix operation.
Abstract: A fast band-limited signal extrapolation technique is presented where the total extrapolation process is achieved by a single matrix operation. The proposed technique and its implementation has many advantages over known extrapolation techniques in terms of computational savings and accuracy of the results, and it can he operated on a realtime basis.
TL;DR: A general synthesis technique is described for obtaining a switched-capacitor (SC) filter from an active RC prototype that permits the processing of signals at much higher frequencies than do previously known circuit design techniques.
Abstract: A general synthesis technique is described for obtaining a switched-capacitor (SC) filter from an active RC prototype. The response of the SC filter is related to that of its prototype by the bilinear z -transform. This allows the filtering and sensitivity properties of the prototype to be preserved for the SC circuit. It also enables the designer to realize such economical and low-sensitivity circuits as the FDNR and gyrator filters. Finally, it permits the processing of signals at much higher frequencies than do previously known circuit design techniques.
TL;DR: Several new structures for the block implementation of HilR digital filters are proposed and the relation between the pole locations of the block structure to that of the original scalar transfer function is derived.
Abstract: Several new structures for the block implementation of HilR digital filters are proposed. The relation between the pole locations of the block structure to that of the original scalar transfer function is derived. A method to obtain the scalar transfer function from a given block structure is described.
TL;DR: In this article, a technique for the design of two-dimensional (2-D) recursive filters with a response that best approximates, in the l_p sense, prescribed magnitude and group delay specifications is proposed.
Abstract: A technique is proposed for the design of two-dimensional (2-D) recursive filters with a response that best approximates, in the l_p sense, prescribed magnitude and group delay specifications. The filter stability is guaranteed through the use of a frequency transformation. The optimization technique used is that of Davidon-Fletcher and Powell. Several examples are given to illustrate the proposed algorithm.
TL;DR: A new approach to optimal design centering, the optimal assignment of parameter tolerances and the determination and optimization of production yield is presented, based upon multidimensional linear cuts of the tolerance Orthotope and uniform distributions of outcomes between tolerance extremes in the orthotope.
Abstract: This paper presents a new approach to optimal design centering, the optimal assignment of parameter tolerances and the determination and optimization of production yield. Based upon multidimensional linear cuts of the tolerance orthotope and uniform distributions of outcomes between tolerance extremes in the orthotope, exact formulas for yield and yield sensitivities, with respect to design parameters, are derived. The formulas employ the intersections of the cuts with the orthotope edges, the cuts themselves being functions of the original design constraints. Our computational approach involves the approximation of all the constraints by low-order multidimensional polynomials. These approximations are continually updated during optimization. Inherent advantages of the approximations which we have exploited are that explicit sensitivities of the design performance are not required, available simulation programs can be used, inexpensive function and gradient evaluations can be made, inexpensive calculations at vertices of the tolerance orthotope are facilitated during optimization and, subsequently, inexpensive Monte Carlo verification is possible. Simple circuit examples illustrate worst case design and design with yields of less then 100 percent. The examples also provide verification of the formulas and algorithms.
TL;DR: In this article, the class of two-dimensional (2D) digital transfer functions which possess quadrantal symmetry in their frequency responses is derived and application of this class in the design of 2-D recursive digital filters is indicated.
Abstract: The class of two-dimensional (2-D) digital transfer functions which possess quadrantal symmetry in their frequency responses is derived. Application of this class in the design of 2-D recursive digital filters is indicated.
TL;DR: In this article, a unified view of sampled-data charge-conserving circuits for analog-to-digital (A/D) and digital-toanalog (D/A) converters and audio frequency filters is presented.
Abstract: Precision analog integrated circuits may be realized using MOS transistors and accurately ratioed MOS capacitors. Compatibility with high-density digital MOS circuits leads to the possibility of fully Integrated subsystems employing both analog and digital circuitry. This paper presents a unified view of sampled-data charge-conserving circuits for analog-to-digital (A/D) and digital-to-analog (D/A) converters and audio frequency filters.
TL;DR: In this paper, the existence, calculation, and use of the simplest generalized inverse are discussed, and generalized inverses are applied to solving underdetermined and overdetermined systems of equations, specifically those that arise in linear control problems.
Abstract: Various kinds of matrix-generalized inverses are defined and classified. Theorems on the existence, calculation, and use of the simplest generalized inverse are stated. Matrices of functions receive special attention. Generalized inverses are applied to solving underdetermined and overdetermined systems of equations, specifically those that arise in linear control problems. Simple examples illustrate suggested procedures.
TL;DR: Various A/D and D/A conversions architectures, as evolved for communication oriented and computer related instrumentation, are described, and their relative advantages and disadvantages reviewed.
Abstract: Various A/D and D/A conversions architectures, as evolved for communication oriented and computer related instrumentation, are described, and their relative advantages and disadvantages reviewed. Important parameters of performance are defined, and a number of critical factors involved in the design of A/D converters are considered. Emphasis is placed on the need for realistic "error budgets" and a recognition of the uncertainties and harsh realities of the environment in place. A number of A/D and D/A converter applications are reviewed to illustrate the diversity of requirements to be met by conversion system designers.
TL;DR: In this paper, the authors present two approaches to the design of residue-to-analog converters to be used with residue number filters, based on mixed radix number system and Chinese remainder theorem.
Abstract: Recent papers have reported that the use of residue number coding in digital filters can result in better speed/cost ratios when compared to filters designed with conventional adders and multipliers. This paper presents two approaches to the design of residue-to-analog converters to be used with residue number filters. The first approach, based on the associated mixed radix number system, is particularly useful when it is desired to translate the residue samples directly into analog form. The second approach, based on the Chinese remainder theorem, is a more direct method for translating from residue to weighted binary representation. A hardware feasibility model is described that was constructed to demonstrate the conversion principles.
TL;DR: In this article, a sigma-delta modulator system is discussed as an alternative to the dual-slope converter and a simple auto-zero circuit and cold switching of the gain setting can be obtained.
Abstract: A sigma-delta modulator system is discussed as an alternative to the dual-slope converter. A simple auto-zero circuit and cold switching of the gain setting can be obtained. The implementation of the analog system in the form of two bipolar IC's offers an attractive application as a multi-input data acquisition system with a scanning capability. A combination with a D/A converter increases the resolution with a small Increase in conversion time. Hardly any accurate elements are required in this application if the dynamic element matching method is used in the D/A converter.
TL;DR: In this paper, a graph theoretic decomposition technique is used to transform large-scale systems into an interconnection of strongly connected components (subsystems), and the analysis of the overall interconnected system is then accomplished in terms of the qualitative properties of the subsystems (strongly connected components) and the stability preserving properties of system interconnections.
Abstract: New Lyapnnov results for uniform asymptotic stability, exponential stability, Instability, complete instability, and uniform ultimate boundedness of solutions for a class of interconnected systems described by nonlinear time-varying ordinary differential equations are established. The present results make use of graph theoretic decomposition techniques to transform large-scale systems into an interconnection of strongly connected components (subsystems), and they also make use of the properties of stability preserving mappings. The analysis of the overall interconnected system is then accomplished in terms of the qualitative properties of the subsystems (strongly connected components) and the stability preserving properties of the system interconnections. A typical result is of the following form. If every subsystem (strongly connected component) is uniformly asymptotically stable and if all system interconnections are stability preserving, then the overall interconnected system is uniformly asymptotically stable. To demonstrate the applicability of these results to physical systems, a specific example is considered. The principal advantages of the present method over existing Lyapunov results for interconnected systems are as follows. 1) The present results make it possible to address the "largeness" of complex systems, since the identification of the strongly connected components (subsystems) can be accomplished by means of efficient computer algorithms. 2) The present stability results are applicable to interconnected systems with unstable subsystems (i.e., the original nontransformed system description may involve unstable subsystems). The main disadvantages of the present method over many existing Lyapunov results are the following. 1) The analysis is not accomplished in terms of the original system structure. 2) When a system consists of only one strongly connected component, the present method cannot be used to advantage, while other methods may.
TL;DR: In this article, coupled van der Pol oscillators containing a fifth-order conductance characteristic are analyzed using a method due to Endo and Mori, and it is shown that for a certain range of parameters double modes are possible for two oscillators, which is in contrast to the case of conventional van der pol dynamics.
Abstract: Coupled van der Pol oscillators containing a fifth-order conductance characteristic are analyzed using a method due to Endo and Mori. This structure has been proposed for modeling the myoelectrical activity of the human large intestine since it produces stable conditions of zero, two single-mode frequencies, and also a double-mode condition. The paper first considers the case of oscilators having equal frequencies and it is shown that for a certain range of parameters double modes are possible for two oscillators, which is in contrast to the case of conventional van der Pol dynamics. The theoretical results have been experimentally verified using both analog simulations and electronic circuitry. In digestive tract modeling, the coupled oscillators must often have unequal intrinsic frequencies and this case is also considered and shown to give similar but more complex parameter conditions for the establishment of double modes.
TL;DR: In this paper, it was shown that every rational transfer function matrix has a right-coprime factorization in √ Q √ n √ times n, and that such factorizations contain all the information about the domain and range of an unstable operator.
Abstract: In this paper, we prove that every rational transfer function matrix has a right-coprime factorization in {\cal Q}^{n \times n} , and that a right-coprime factorization contains all the information about the domain and range of an unstable operator. We also derive a general necessary and sufficient condition for feedback stability that is applicable even to nonlinear systems, and show that right-coprime factorizations arise naturally when this general condition is applied to linear time-invariant systems.
TL;DR: This letter presents a more successful technique based on a mixed-radix conversion process that can be built using commercially available elements and requires shorter word lengths in the ROM which stores the output function.
Abstract: In a recent issue of this journal, a hardware implementation of the Chinese Remainder Theorem was proposed for the translation of residue coded outputs into natural integer for an FIR filter realization. The method requires a modulo M adder-shifter network which is not commercially available and has to be constructed from more basic logic elements. This letter presents a more successful technique based on a mixed-radix conversion process. The residue to binary decoder can be built using commercially available elements and requires shorter word lengths in the ROM which stores the output function.
TL;DR: In this paper, the authors developed a design technique for approximating nonseparable frequency characteristics by sums and products of separable transfer functions, called the piecewise separable decomposition of the characteristic.
Abstract: The present paper develops a design technique for approximating nonseparable frequency characteristics by sums and products of separable transfer functions. This approximation is called the "piecewise separable" decomposition of the characteristic. In the design technique, the desired filter with half-plane symmetry (radial symmetry) is obtained by shifting a low-pass characteristic in the frequency domain, and by combining these shifted characteristics. Also the paper includes design approaches for the four-quadrant symmetry filters. Two examples illustrate the technique of the paper.
IBM1
TL;DR: In this article, a matrix power algorithm for enumerating all simple paths in a graph using Warshail's Theorem was proposed, which uses O(N 2 3 ) matrix operations.
Abstract: Warshail's Theorem is used to obtain a matrix power algorithm for enumerating all simple paths in a graph The algorithm uses O(N^{3}) matrix operations, compared to O(N^{4}) operations for previous algorithms