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ABSTRACT: Based on least-squares approximation of the rectangular pulse (Vilbeacute , 1999) by exponential functions, this brief presents an alternative method for performing numerical inversion of the Laplace transform. It compares favourably with the celebrated Vlach's method
Circuits and Systems II: Express Briefs, IEEE Transactions on 07/2006; · 1.41 Impact Factor
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ABSTRACT: In this paper we present a technique for generating low complexity equivalent circuit models for VLSI circuit interconnects via the Laguerre-Gram model order reduction (MOR) method developed by our team. We discuss model passivity and equivalent circuit implementation and then show the advantages of our method in preserving important signal parameters such as rise time, delay and overshoot
Signal Propagation on Interconnects, 2006. IEEE Workshop on; 06/2006
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Signal Processing. 01/2006; 86:3486-3489.
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ABSTRACT: We present an efficient model reduction procedure based on the Laguerre description of the system to be approximated. Using a one-order operator defined in the Laplace domain we construct a pencil of functions and formulate the problem as the minimization of the L<sub>∞</sub><sup>2</sup>(R<sup>+</sup>) criterion. The use of a weight function in the inner product definition allows a control of the time-error spreading in model reduction procedure. We show how the required Gram matrix can be computed efficiently and prove that the impulse response of the reduced model is also in L<sub>∞</sub><sup>2</sup>(R<sup>+</sup>). The transfer function approach allows an immediate and promising application in model reduction of infinite dimensional systems. An extension to multiple-input-multiple-output systems is also given.
IEEE Transactions on Automatic Control 10/2005; · 2.11 Impact Factor
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Research in Microelectronics and Electronics, 2005 PhD; 08/2005
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ABSTRACT: The VLSI (very large scale integration) industry has the tendency to decrease circuit size, increase speed, assuring ever lower energy consumption and ever higher integration density of analogical components accompanied by digital blocks. With this tendency circuit designers are faced with a new challenge: the analysis and modeling of logical and analogical signals propagating between two circuit points. The search for high speed applications makes the effects of interconnects, usually neglected in the past, an important issue; noise, delay, distortion, reflections and cross talk are just some of these effects. High integration density, miniaturization, high working frequencies are three great factors which prevent interconnects to be considered small independent circuits. Thus, simulation becomes a rather difficult task. Still, wouldn't it be possible to replace complete interconnect equivalent circuits by simpler and more flexible models. Our new model-order reduction technique is mainly based on the use of the Laguerre representation and a simple operator used to generate an approximation base.
Signal Propagation on Interconnects, 2005. Proceedings. 9th IEEE Workshop on; 06/2005
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ABSTRACT: An efficient method for evaluating inner products of repeated integrals and derivatives of a function described by a Laguerre model is presented. An immediate and promising application is model reduction of infinite-dimensional transfer functions.
Signal Processing. 01/2005;
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ABSTRACT: It has become well accepted that interconnect delay dominates gate delay in current VLSI circuits. This paper introduces a new method, based on a frequency domain approach, for the simulation of interconnect problems found in high speed digital circuits and SOC-AMS.
Signal Propagation on Interconnects, 2004. Proceedings. 8th IEEE Workshop on; 06/2004
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ABSTRACT: In the context of RF and high-speed circuits, Systems On Chip with Analog and Mixed Signals (SOC-AMS), interconnect has becoming a dominant factor in determining circuit performance and reliability in deep submicron designs. Transmission line properties of on-chip wiring need to be taken into account due to the great lengths and fast rise times encountered. Coupling noise between adjacent interconnects can also cause catastrophic effects on the logical functionality and long-term reliability of a VLSI circuit. With these trends, the electrical phenomena that have to be investigated are governed by the electromagnetic theory. However, it's impossible to proceed to a complete SOC - AMS analysis with a full wave electromagnetic numerical tool, due to the large scale integration. As interconnects are typically of very large size and high-order, model-order reduction becomes necessary for efficient SOC modeling, simulation, design and optimization. In this communication, a new method based on numerical inversion of Laplace transform and on a discrete model-reduction technique is presented for simulating peak crosstalk noise problems found in high speed digital circuits and SOC-AMS. The method, particularly efficient and easy to be implemented in a program, is useful for an electromagnetic simulation of a complete system.
Microwave Conference, 2003. 33rd European; 11/2003
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ABSTRACT: Kautz functions have received much attention in the recent
mathematical modeling and identification literature. These functions
which involve free parameters can approximate efficiently signals with
strong oscillatory behavior. We consider here the choice of the free
parameters in discrete (two-parameter) Kautz approximation. Using a key
relationship between Kautz and Laguerre expansions we derive an upper
bound for the quadratic truncation error. Minimization of this upper
bound yields pertinent parameters, whose computation then requires
reduced knowledge of the function to be modeled
IEEE Transactions on Automatic Control 06/2002; · 2.11 Impact Factor
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ABSTRACT: A procedure for determining two parameters to be used in the Kautz approximation is presented. It is based on minimisation of an upper bound of the error energy
Electronics Letters 05/2000; 36(8):769-771. · 0.96 Impact Factor
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ABSTRACT: A new online method to optimize the free parameter in adaptive
Laguerre-based filters is presented, it is based on the minimization of
a criterion that is equivalent to an upper bound for the quadratic
approximation error. The proposed technique presents a fast convergence
and a good robustness
IEEE Transactions on Signal Processing 05/2000; · 2.63 Impact Factor
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ABSTRACT: Some fundamental properties of an impulse response Gramian for
linear, time-invariant, asymptotically stable, discrete
single-input-single-output (SISO) systems are derived. This Gramian is
system invariant and can be found by solving a Lyapunov equation. The
connection with standard controllability, observability, and cross
Gramians is proven. The significance of these results in model-order
reduction is highlighted with an efficient procedure
IEEE Transactions on Automatic Control 04/2000; · 2.11 Impact Factor
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ABSTRACT: Jain's pencil-of-functions method based on the linear
dependence/independence of a set of functions is revisited. It is shown
that no matter what model order is chosen, every estimated denominator
coefficient may be regarded as the geometric mean of two values obtained
in a least-squares sense
IEEE Transactions on Signal Processing 11/1999; · 2.63 Impact Factor
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ABSTRACT: We report on our investigations to choose a free parameter to
minimize the error energy when approximating a given signal with
orthogonal basis functions. This method requires limited knowledge of
the signal to be approximated and has a low computational cost
IEEE Transactions on Signal Processing 10/1999; · 2.63 Impact Factor
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ABSTRACT: A simplified algorithm for the efficient computation of sequences required in the Laguerre transform signal analysis of transients on uniformly distributed RGC lines is derived
Electronics Letters 09/1999; 35(16):1299-1300. · 0.96 Impact Factor
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ABSTRACT: An optimization technique is provided for the approximation of the
pure time delay. Owing to a near-optimal starting point, the integral
square error is reduced through a few iterations of a Gauss-Newton
process. Compact implementation and robustness should encourage a large
use in various engineering domains
IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications 05/1999;
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ABSTRACT: It is shown that the sequence of polynomials produced during a run
of the extended Euclid's algorithm can be readily obtained via the
non-extended algorithm, when properly initialised
Electronics Letters 06/1997; · 0.96 Impact Factor
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ABSTRACT: A novel noniterative method is presented for deriving
reduced-order models of linear discrete-time systems without solving any
nonlinear equation. The resulting error energy is usually relatively
close to optimal
Electronics Letters 09/1996; · 0.96 Impact Factor
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ABSTRACT: This correspondence investigates the choice of a free parameter,
usually related to time scale, that minimizes the error energy when
approximating a given signal with some widely used orthonormal basis
functions. The proposed solution is the best that can be achieved with
the limited required knowledge of the signal. It is appealing for
experimental data for which no exact mathematical expression is
available
IEEE Transactions on Automatic Control 11/1995; · 2.11 Impact Factor
