Showing papers in "IEEE Transactions on Circuits and Systems in 2002"

Consistency of a time-stepping method for a class of piecewise linear networks

Abstract: In this brief, we will study the computation of transient solutions of a class of piecewise-linear (PL) circuits. The network models will be so-called linear complementarity systems, which can be seen as dynamical extensions of the PL modeling structure. In particular, the numerical simulation will be based on a time-stepping method using the well-known backward Euler scheme. It will be demonstrated, by means of an example, that this widely applied time-stepping method does not necessarily produce useful output for arbitrary linear dynamical systems with ideal diode characteristics. Next the consistency of the method will be proven for PL networks that can be realized by linear passive circuit elements and ideal diodes by showing that the approximations generated by the method converge to the true solution of the system in a suitable sense. To give such a consistency proof, a fundamental framework developed previously is indispensable as it proposes a precise definition of a "solution" of a linear complementarity system and provides conditions under which solutions exist and are unique

Wavelet-based Optical Flow Estimation

Abstract: In this paper, a new algorithm for accurate optical flow estimation using discrete wavelet approximation is proposed. The proposed method takes advantages of the nature of wavelet theory, which can efficiently and accurately represent \"things\", to model optical flow vectors and image related functions. Each flow vector and image function are represented by linear combinations of wavelet basis functions. From such wavelet-based approximation, the leading coefficients of these basis functions carry the global information of the approximated \"things\". The proposed method can successfully convert the problem of minimizing a constraint function into that of solving a linear system of a quadratic and convex function of wavelet coefficients. Once all the corresponding coefficients are decided, the flow vectors can be determined accordingly. Experiments conducted on both synthetic and real image sequences show that our approach outperformed the existing methods in terms of accuracy.

On the dynamic analysis of piecewise-linear networks

Abstract: Piecewise-linear (PL) modeling is often used to approximate the behavior of nonlinear circuits. One of the possible PL modeling methodologies is based on the linear complementarity problem, and this approach has already been used extensively in the circuits and systems community for static networks. In this paper, the object of study is dynamic electrical circuits that can be recast as linear complementarity systems, i.e. as interconnections of linear time-invariant differential equations and complementarity conditions (ideal diode characteristics). A mathematically precise framework is developed that formalizes the mixed discrete and continuous behavior of these switched networks. Within this framework, the fundamental question of well-posedness (existence and uniqueness of solution trajectories given an initial condition) is studied and additional properties of the behavior are derived. For instance, a full characterization is presented of the inconsistent states

A new architecture for implementing pipelined FIR ADF based on classification of coefficients

Abstract: In this paper, we propose a new method for implementing pipelined finite-impulse response (FIR) adaptive digital filter (ADF), with an aim of reducing the maximum delay of the filtering portion of conventional delayed least mean square (DLMS) pipelined ADF. We achieve a filtering section with a maximum delay of one by simplifying a pre-upsampled and a post-downsampled FIR filter using the concept of classification of coefficients. This reduction is independent of the order of the filter, which is an advantage when the order of the filter is very large, and as a result the method can also be applied to infinite impulse response (IIR) filters. Furthermore, when the proposed method is compared with the transpose ADF, which has a filtering section with zero delay, it is realized that it significantly reduces the maximum delay associated with updating the coefficients of FIR ADF. The effect of this is that, the proposed method exhibits a higher convergence speed in comparison to the transpose FIR ADF.

Tensor function analysis of quantized chaotic piecewise-affine pseudo-Markov systems-I : Second-order correlations and self-similarity

Abstract: For pt. I see ibid., vol. 49, pp. 137-49 (2002).The general approach developed in the companion paper for the statistical analysis of trajectories produced by a class of chaotic systems generalizing the classical view of piecewise-affine Markov maps is here applied to the computation of higher order correlations. For any given order m, a procedure is given to write a closed form expression in the z-transformed domain for the mth dimensional tensor encoding the contribution of the system dynamics to the correlation functions of that order. After having defined and discussed a suitable generalization of the concept of second-order self-similarity, we finally use this general procedure to show that simple chaotic maps may exhibit highly nontrivial behaviors also in their higher order statistics.