bluuebunny/crossref_metadata_2025_split huggingface dataset:
The overdamped double‐scroll family. Part I: Piecewise‐linear geometry and normal form
Authors: Silva Christopher P. , Chua Leon O. 
Published: July 2007

AbstractThis paper is the first part of a two part work that aims to introduce a new family of piecewise‐linear differential equations that exhibit chaotic behaviour in numerical simulations and to provide a rigorous mathematical proof of its chaotic nature.The new family presented here has the same eigenvalue distribution as the well‐known Lorenz equations in its chaotic regime but has a different symmetry. It is a derivative of the recently investigated double‐scroll family of piecewise‐linear differential equations.1 It differs, however, from the double‐scroll family in that its members have all real eigenvalues at the origin. In particular, since the associated eigenspace Es(0) is similar to that of an overdamped linear circuit, we will henceforth refer to this family as the overdamped double‐scroll family.We establish Chua's circuit2 as a member of this family under appropriate conditions. Preliminary numerical simulations exhibit some interesting phenomena such as period‐doubling, periodic windows between chaotic behaviour, and strange attractors of differing geometric structure.Our approach in the rigorous analysis will be that employed for the double‐scroll family in Reference 1. We derive a linearly equivalent class of piecewise‐linear differential equations which includes the family simulated numerically as a special case. the necessary and sufficient condition for two piecewise‐linear vector fields belonging to this new overdamped double‐scroll family to be linearly equivalent is that their respective eigenvalues at respective equilibrium points be scalar multiples of each other. If the scalars are all identity, then we have linear conjugacy of the vector fields. an explicit normal form equation, in the sense of global bifurcation, is presented that is parametrized by its own eigenvalues.We find that linearly equivalent vector fields associated with the overdamped double‐scroll family exhibit the same global behaviour even though their equivalence is based on the local concept of normalized eigenvalues. In addition, the piecewise‐linear differential equations associated with these equivalent vector fields can be quite different from each other.
Parallel processing for analogue fault diagnosis
Authors: Wey Chin‐Long 
Published: July 2007

AbstractThe computer‐aided testing (CAT) problem is inherently a large scale systems problem, it is essential to exploit whatever computational power is available to reduce the computational requirements for both on‐line and off‐line test processes. In particular, digital CAT algorithms often use some degree of parallel processing in their implementation. Therefore, the degree to which an analogue CAT algorithm can be implemented in parallel becomes a significant factor in determining its viability.In this paper, a parallel test algorithm and the associated architecture for the test system for analogue circuits and systems are proposed. the proposed test algorithm is applicable to testing multiple faults. Based on a combinatorial covering set approach, the conditions for the non‐sequential execution of the test algorithm is analysed and the parallel processing to generate the test results is also addressed.Although this paper is motivated on the discussions of analogue fault diagnosis, the proposed parallel algorithm and the combinatorial covering approach can also be applied to digital testing.
A neural network approach to transform image coding
Authors: Chua L. O. , Lin T. 
Published: July 2007

AbstractA neural network approach is presented for transform image coding. It is shown that the three steps in the conventional transform image coding, i.e. the unitary transform of spatial domain image data, the quantization of the transform domain data and the binary coding of the quantized data, can be unified into a one‐step optimization problem. Then, the optimization problem is solved by an appropriately constructed Hopfield neural network whose input is the spatial domain image data and whose output is binary codes. A practical circuit implementation is given to perform the transform image coding. the circuit has rM2 neurons, where r is the bit‐rate, in bit/pixel, of the coding and M2 is the size of the images. Each neuron consists of only a non‐linear voltage amplifier, a linear voltage‐controlled current source, a d.c. current source, a linear passive resistor, a linear passive capacitor, and a weighted voltage summer which can be made of a single op amp with some linear passive resistors. Moreover, each neuron is locally connected with no more than b ‐ 1 other neurons by wires, where b is the maximum bit allocated to a transform domain coefficient. Therefore, our proposed approach is particularly suitable for low‐bit‐rate image coding and VLSI implementation. Furthermore, the analogue and parallel nature of our approach matches perfectly the high‐speed requirement of real‐time image coding.
Simulated‐annealing‐based optimization of coefficient and data word‐lengths in digital filters
Authors: Catthoor Francky , de Man Hugo , Vandewalle Joos 
Published: July 2007

AbstractThe accurate characterization of worst‐case limit‐cycle behaviour and other finite word‐length effects in digital filters constitutes a challenging and important optimization application. Indeed, for a chip implementation this can lead to a significant reduction in the signal word‐length and hence to considerable savings in terms of the final chip area. This paper describes a new and accurate method for this investigation which is based on a simulated annealing procedure with a general scope. Novel methods for dynamically and efficiently updating the essential parameters of the annealing schedule keep the required CPU times reasonable.The quality of the results obtained with our optimization routine and the general applicability of our approach are further substantiated with some promising results for the quantization of coefficients in arbitrary digital filters.
Graphs in floor‐plan design
Authors: Otten Ralph H. J. M. 
Published: July 2007

AbstractGraph models play an important role in floor‐plan design. In this paper the relations between the various models are investigated. Useful graph‐theoretical facts are presented in this context, and their application is discussed. Special attention is given to the implications of structural restraints, for the models as well as for the applications, geometrical optimization and global routing in particular.
Module placement for large chips based on sparse linear equations
Authors: Tsay Ren‐Song , Kuh Ernest S. , Hsu Chi‐Ping 
Published: July 2007

AbstractThere are many algorithms for automatic placement in IC layout design. However, as chips become increasingly larger and more complex, existing algorithms are no longer suitable. One major drawback in existing algorithms is that the sparsity inherent in the placement specification has not been taken into consideration properly.In this paper, we propose an efficient method of module placement for large and highly complex chips by repeatedly solving sparse linear equations. the resistive network analogy of the placement problem and the convexity of the objective function play a major role in our approach. Our method employs the SOR (successive over‐relaxation) method to solve the linear equations and uses a top‐down hierarchy in partitioning the chip. We have also devised an effective BGS (block Gauss‐Seidel) iteration scheme to achieve global optimum results.The method has been implemented and tried with a number of real chips. For a triple‐metal‐layer, 100K sea‐of‐gates with 26,000 instances, it takes 50 min on a VAX 8650 and yields excellent results in terms of total wire length.
An efficient algorithm for two‐ and three‐dimensional IC floor planning
Authors: Kyung C. M. , Lee P. H. , Yang Y. Y. , Park I. C. 
Published: July 2007

AbstractThis paper proposes a new procedure for floor planning of VLSI chips in two‐ and three‐dimensional space using the so‐called ‘scatter‐and‐gather’ approach. In the ‘scattering’ phase of this approach, dots denoting the mass centre of each functional block are ‘scattered’ in 2‐D space using FDR (force‐directed relaxation), UCG (unconstrained cluster growth) or CCG (constrained cluster growth) techniques.The ‘gathering’ phase is modelled as a computational geometrical problem called MBE (minimal box embedding), for which two practical solution techniques, GBS (growing box scheme) and RBS (reducing box scheme) are described. the 2‐D MBE problem is to find the orientation, shape and size of a rectangle which has the smallest area among those rectangles which stay within the specified aspect ratio range and include (gather), at least, the specified fraction of dots scattered in 2‐D space. Several speed‐up techniques such as incremental transform/sorting and quadrant folding are also explained. It is shown through experiment that the UCG has advantages over FDR in terms of CPU time and the degree of correlation between the area of the minimum embedding box and the routing length.The proposed MBE algorithm has been extended to the layer assignment of circuit modules in truly three‐dimensional package planning where the circuit modules are placed on multiple layers and inter‐layer connections are allowed in the interior of each layer plane. Experimental results on 2‐D and 3‐D examples have shown that the MBE algorithm is at least 20 times faster than simulated annealing (SA) in the 2‐D case, and min‐cut‐based layering plus force‐cut placement in the 3‐D case. On the other hand, the routeing length overhead of the MBE algorithm was about 30‐40 per cent in the 2‐D case compared to SA, and only 10 per cent in the 3‐D case compared to min‐cut layering followed by the force‐cut placement technique.
Maximally linear FIR digital differentiators for midband frequencies
Authors: Kumar B. , Dutta Roy S. C. 
Published: July 2007

AbstractAmong the known FIR digital differentiators, the minimax relative error (MRE) approximations are the most efficient ones, where the weighting coefficients are derived by using an optimization algorithm. This approximation fails at the frequency ω = π if the order N of the differentiator is odd. A half sample advance (i.e. a delay τ = −1/2) and an even N become necessary to extend the MRE approximation up to ω = χ; these are, however, undesirable features, particularly in large signal processing systems. This paper proposes digital differentiators, which are characterized by maximal linearity of the frequency response at the midband frequency ω = π/2, and gives a mathematical relation for the weighting coefficients. the order N of the differentiator has been ensured to be odd, and no half sample advance has been used. It has been shown that for relative error (RE) ⩽ 1 per cent, the proposed differentiators are more efficient as compared to those based on the MRE approximation, in terms of multiplications required per sample of the input signal for all N (N odd). the proposed approximations are also capable of giving extremely low RE (10−3 to 10−6 per cent), for narrow midband frequencies, with attractively low order N.
Cascade decomposition of a passive 2n‐port network
Authors: Uruski M. 
Published: July 2007

AbstractThis paper deals with a cascade decomposition of a passive 2n‐port network. after a basic discussion relative to complex‐ and unit‐normalized scattering matrices, necessary and sufficient conditions are presented under which given lossless 2n‐ports D1 and D2 are simultaneously extractable from the front‐ and back‐ends of the passive 2n‐port N, respectively, to leave a passive 2n‐port remainder Ne. Based on these conditions, some relations between the individual and simultaneous extractability of D1 and D2 from N for both degenerate and non‐degenerate remainders Ne are discussed. the results are presented in terms of scattering as well as impedance matrices and can be considered as an extension of those given in Reference 1.
‘Lorenz attractor’ from an electrical circuit with uncoupled continuous piecewise‐linear resistor
Authors: Tokunaga R. , Komuro M. , Matsumoto T. , Chua L. O. 
Published: July 2007

AbstractWe present a simple piecewise‐linear circuit which exhibits a chaotic attractor similar to that observed from the well‐known Lorenz equation. Whereas the non‐linearities in the Lorenz equation consists of two product terms between two state variables, the non‐linearities in our circuit consists of two ‘uncoupled’ 2‐terminal continuous non‐linear resistors, each characterized by a 2‐segment v‐i characteristic.Both experiments and computer simulations of this circuit confirm a Lorenz‐like strange attractor. the nature of the trajectories associated with this attractor is analysed and explained with the help of the circuit's piecewise‐linear‐geometry.
Design of odd‐degree linear‐phase sampled‐data bandpass filters with equiripple amplitude response
Authors: Fahmy M. F. , Abo‐Zahhad M. , Sobhy M. I. 
Published: July 2007

AbstractThis paper presents a novel approach for the design and synthesis of odd‐degree sampled‐data filters. Initially, an efficient iterative scheme is described for the construction of a class of selective linear‐phase distributed bandpass filters with equiripple passband loss response. Then, the filter's transfer function is synthesized using classical distributed circuit networks. Finally, the equivalent switched‐capacitor filter could be constructed. the resulting switched‐capacitor networks are completely insensitive w.r.t. parasitic capacitances, as well as having low Cmax/Cmin Design tables and an illustrative example are also given.
Pseudopassive two‐dimensional recursive digital filters for image processing
Authors: Domanski Marek , Fettweis Alfred 
Published: July 2007

AbstractThis paper describes the theory of two‐dimensional digital filters that are pseudopassive with respect to the lp‐norm of the state vector. As the classical pseudopassive digital filters are a subclass of these filters, the respective theorems referred to stability are also generalized. It is shown that this theory is useful for the two‐dimensional filters that answer with non‐negative‐valued responses to non‐negative‐valued excitations. Such systems are especially suitable for image processing. the synthesis of the l1‐pseudolossless systems is proposed as a tool to guarantee stability of such filters. A technique to obtain local state‐space models for such two‐dimensional l1‐pseudolossless recursive filters with prescribed spatial responses is given. A ‘Gaussian filter’ design illustrates the technique and shows that the proposed two‐dimensional l1‐pseudolossless filters are able to match useful spatial responses.
Fault prediction process for large analogue circuit networks
Authors: Jiang Ben‐Lu , Wey Chin‐Long 
Published: July 2007

AbstractTo make the existing fault diagnosis algorithms suitable and feasible for practical large analogue networks, a large network must be decomposed into small uncoupled subnetworks. Recently, an efficient decomposition approach fault diagnosis process has been proposed by Bandler et al. This approach keeps both the computations and measurements to acceptable bounds. However, the error effect due to component tolerance in practical circuits may drastically affect the identification of the faulty components. In this paper, a fault prediction approach fault diagnosis process is presented to diagnose precisely the faulty components. the result of this study shows that error effect can be alleviated significantly if the network can be continuously monitored. the proposed fault prediction approach results a significant improvement in both computation and error effect over the original decomposition approach.
Design of two‐dimensional pseudolossless digital filters with prescribed spatial responses
Authors: Domanski Marek 
Published: July 2007

AbstractThe paper presents a technique to compute the parameters of the state‐space model of the two‐dimensional pseudolossless (e.g. wave or orthogonal) digital filter that best approximates a given spatial response. the search for the optimal solution is performed using an unconstrained optimization algorithm with reduced number of parameters. the optimization variables are the elements of the upper triangle of a skew‐symmetric matrix which is related to the orthogonal system matrix by the Cayley formula. Thus the resulting system is always stable.
On the development of symmetrically stabilized five‐phase oscillators and some implications
Authors: Kaplan B. Z. , Yardeni D. 
Published: July 2007

AbstractThe paper deals with the development of a symmetrically stabilized five‐phase oscillator. the development results from two origins. It employs on one hand a five‐phase conservative oscillator. On the other hand the stabilization process of the oscillator is due to similar non‐linear damping terms in earlier developments of stabilized three‐phase oscillators. A new feature of the present system is that it possesses an interesting steady state limit‐cycle behaviour. the two possible steady state oscillations are similar, since both of them consist of a five‐phase balanced set of phasors which are arranged symmetrically. However, each mode of possible steady state oscillation possesses its own unique frequency, although the amplitudes are equal. Another interesting feature of the oscillator is related to the way in which the various possible solutions (oscillatory, steady state, stable and unstable dynamic behaviours) evolve from initial conditions. There seem to exist regions where the system solutions appear sensitive to minute changes in initial conditions. It appears that completely different types of dynamic behaviours can develop from initial conditions in close proximity, which may lead eventually to the development of slightly modified systems with chaotic dynamics. the paper concludes by suggesting an application of multiphase oscillators for feeding phased array antennas.
Steady‐state response of non‐linear circuits: A frequency‐domain relaxation method
Authors: Ushida A. , Chua L. O. 
Published: July 2007

AbstractWe propose here an efficient algorithm for finding the steady‐state response of stiff non‐linear circuits. It is based on a frequency‐domain relaxation method and can be applied efficiently to obtain the steady‐state waveforms of both periodic systems and multi‐frequency‐component systems. the solution at each iteration is obtained by solving an associated linear time‐invariant circuit at every frequency component via modified nodal analysis. Our algorithm is very simple and can be applied efficiently to solve a large class of practical non‐linear communication circuits which are notoriously stiff and hence rather time‐consuming to solve with existing methods.
Bifurcation analysis of a cusp‐constrained piecewise‐linear circuit
Authors: Tokunaga Ryuji , Chua Leon O. , Matsumot Takashi 
Published: July 2007

AbstractThis paper gives a detailed bifurcation analysis of a cusp‐constrained circuit in terms of the quantity ‘rotation‐jump ratio’. This turns out to be a very natural quantity to analyse various interesting bifurcation phenomena observed in the circuit.
Simultaneous amplitude and phase approximation for fir filters
Authors: Leeb F. , Henk T. 
Published: July 2007

AbstractAn FIR filter design method with simultaneous amplitude and phase approximation is presented. Two components are proposed in the design method: simultaneous amplitude and phase interpolation in the passband and amplitude interpolation in the stopband. These interpolations are implemented by the Remez exchange algorithm.The polynomials for the interpolations are generated by recurrence formulae and the recurrence coefficients are calculated by a recursive method. the properties of the filters designed with the simultaneous approximation are investigated and compared with those of exact linear and minimum phase filters.
Cmos latchup theory
Authors: Deng A. C. , Chua L. O. 
Published: July 2007

AbstractThe purpose of this paper is to study the CMOS latchup phenomenon from a non‐linear circuit theoretic standpoint by using some recently developed results on negative‐resistance devices. We introduce a simple mechanism to describe the latchup phenomenon based on a special circuit topology called feedback structure, which is shown to be responsible for the occurrence of latchup. Several guidelines are proposed to prevent latchup by destroying the feedback structure. In addition to the characterization of the steady‐state behaviour, we use a first‐order circuit model to analyze the latchup dynamics during the turn‐on process and give a stability analysis of the circuit dynamics. All existing techniques to prevent latchup are shown to follow naturally from our guidelines, which are derived using nonlinear circuit theory.
Darlington's theorem and complex normalization
Authors: Pauli Rainer 
Published: July 2007

AbstractTwo novel proofs are presented to establish the equivalence between complex normalization and Darlington representation of the loads. Schwarz reflection of analytic functions and Hermitian metrics serve in these proofs as natural concepts for the analysis of lossless multiports. By use of these tools, the algebraic structure that underlies the physical notion of losslessness is analysed, and a class of matrix representations of lossless 2n‐ports is derived. the fundamental transformations between these matrices are established to facilitate easy conversion of results related to different choices of co‐ordinates (voltages/currents, waves, impedances, reflectances). By virtue of this theory, complex normalization is tacitly extended to include not only impedances but also reflectances as references. Explicit expressions for a 2n‐port normalized to complex loads are derived. Invariance of the complex normalized scattering matrix in a lossless cascade circuit is shown to be the most comprehensive generalization of the well known invariance of scalar reflection magnitudes. the relation between this viewpoint and the general theory of invariants of linear fractional maps in terms of cross‐ratios is pointed out explicitly. the factorization problem, common to complex normalization as well as Darlington representations, is also reviewed, and it is shown that the concept of minimal factorization (well known in linear prediction theory) leads to more satisfactory results than those of established factorization recipes in complex normalization.
The large‐change sensitivity network
Authors: Aeyels Dirk , Wlllems Jacques L. 
Published: July 2007

AbstractIn this paper the large‐change sensitivity network is introduced as a notion which is helpful in the investigation of sensitivity problems. the relation with the small‐change sensitivity network is discussed. Three problems are considered, chosen mainly to illustrate the power of this new concept: for example, we show how the classical Thévenin and Norton theorems follow directly from the large‐change sensitivity network and its properties.
The dynamics of a non‐linear discrete oscillator
Authors: Wu Jingtang , Yang Yongyi 
Published: July 2007

AbstractThe dynamic behaviour of a simple second‐order discrete system with a single non‐linear factor, specified by (x, y)‐ (Ax + B(y + sin(2π(x +y))), x), (A, B) ϵ D = {(A, B): A, B ≥ 0, A + B < 1} ‐ is studied. the parameter subspace of D is analysed in detail. the bifurcation sets of the system are found. the existence of chaos in the system is proved by applying Marotto's theorem. the result of computer simulation agrees well with its analytical counterpart, and confirms that the single non‐linear factor ϕ = sin(2π(x + y)) is indeed the crucial point of a very complicated dynamic behaviour, including the alternative emergence of periodic, quasi‐periodic and chaotic phenomena, of this simple second‐order oscillator.