Time-interleaved oversampling A/D converters: theory and practice

Preface During most of the Twentieth Century, physicists have been mainly concerned with linear dynamics. Despite the works of Poincaré, Birkhoff and von Neumann, the paradigm in physics was linear dynamics. Courses in Classical Mechanics systematically ignored intrinsically non-linear phenomena and chaos, restricting Mechanics to Integrable Systems, i.e., dynamical systems with an underlying Lie group structure, having dynamics that are exponentials of linear algebras. During the second half of the 70's the interest in nonlinear dynamics gradually emerged in physics fueled by the possibility of enriching our intuition using increasingly powerful (as well as popular and affordable) computers. The chaos paradigm took form, with new problems and new ways to analyze nature. An intense development followed the introduction of graphic workstations in the 1980s. Questions such as: How to characterize systems presenting chaotic dynamics? How to compare models with experiments? were then included within the valid questions of the chaos paradigm. By that time it became clear that although there exist only a few different ways of displaying linear behaviour (always present in widely different classes of problems), nonlinear problems presented a large variety of different patterns, as well as other specific features such as sensitivity to initial conditions. The urge to generate some comprehensive understanding of chaos (are there different classes of chaotic behaviour?) became evident. During the '80s, there were several attempts to solve the classification problem. Earlier attempts focused in the routes to chaos, the sequence of bi-furcations as a function of a single control parameter, that lead to chaos in a particular system. By the middle '80s this attempt had proven to be of limited use: there were infinitely many routes to chaos in simple two-WSPC/Book Trim Size for 9in x 6in wsbook viii The User's Approach to Topological Methods in 3-D Dynamical Systems parameter systems. The chaos community then turned its hopes towards fractal dimensions, i.e., a measure of the geometrical imprint (in phase-space) of a chaotic attractor. By the end of the '80s this path had also proven to be almost useless for the characterization/classification problem (although some interesting features such as Barnsley's fractal pictures spun off this effort). The two main directions taken by the chaos community that we just described were not the only explored directions. Around 1987, a third programme aiming to classify low dimensional (3-D) systems using topo-logical orbit organization began. This project in Physics was preceded by at least …