400 research outputs found
The parametric characteristics of frequency response functions for nonlinear systems
The characteristics of the frequency response functions of nonlinear systems can be revealed and analyzed through the analysis of the parametric characteristics of these functions. To achieve these objectives, a new operator is defined, and several fundamental and important results about the parametric characteristics of the frequency response functions of nonlinear systems are developed. These theoretical results provide a significant and novel insight into the frequency domain characteristics of nonlinear systems and circumvent a large amount of complicated integral and symbolic calculations which have previously been required to perform nonlinear system frequency domain analysis. Several new results for the analysis and synthesis of nonlinear systems are also developed. Examples are included to illustrate potential applications of the new results
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Many critical EDA problems suffer from the curse of dimensionality, i.e. the
very fast-scaling computational burden produced by large number of parameters
and/or unknown variables. This phenomenon may be caused by multiple spatial or
temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit
simulation), nonlinearity of devices and circuits, large number of design or
optimization parameters (e.g. full-chip routing/placement and circuit sizing),
or extensive process variations (e.g. variability/reliability analysis and
design for manufacturability). The computational challenges generated by such
high dimensional problems are generally hard to handle efficiently with
traditional EDA core algorithms that are based on matrix and vector
computation. This paper presents "tensor computation" as an alternative general
framework for the development of efficient EDA algorithms and tools. A tensor
is a high-dimensional generalization of a matrix and a vector, and is a natural
choice for both storing and solving efficiently high-dimensional EDA problems.
This paper gives a basic tutorial on tensors, demonstrates some recent examples
of EDA applications (e.g., nonlinear circuit modeling and high-dimensional
uncertainty quantification), and suggests further open EDA problems where the
use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and
System
Mapping from parametric characteristics to generalized frequency response functions of nonlinear systems
Based on the parametric characteristic of the nth-order GFRF (Generalised Frequency Response Function) for nonlinear systems described by an NDE (nonlinear
differential equation) model, a mapping function from the parametric characteristics to the GFRFs is established, by which the nth-order GFRF can directly be written into a
more straightforward and meaningful form in terms of the first order GFRF, i.e., an ndegree polynomial function of the first order GFRF. The new expression has no recursive
relationship between different order GFRFs, and demonstrates some new properties of the GFRFs which can explicitly unveil the linear and nonlinear factors included in the GFRFs, and reveal clearly the relationship between the nth-order GFRF and its parametric characteristic, and also the relationship between the nth-order GFRF and the
first order GFRF. The new results provide a novel and useful insight into the frequency domain analysis and design of nonlinear systems based on the GFRFs. Several examples are given to illustrate the theoretical results
Functional sets with typed symbols: Framework and mixed Polynotopes for hybrid nonlinear reachability and filtering
Verification and synthesis of Cyber-Physical Systems (CPS) are challenging
and still raise numerous issues so far. In this paper, an original framework
with mixed sets defined as function images of symbol type domains is first
proposed. Syntax and semantics are explicitly distinguished. Then, both
continuous (interval) and discrete (signed, boolean) symbol types are used to
model dependencies through linear and polynomial functions, so leading to mixed
zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes
with typed symbols. Polynotopes can both propagate a mixed encoding of
intervals and describe the behavior of logic gates. A functional completeness
result is given, as well as an inclusion method for elementary nonlinear and
switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a
hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a
stochastic uncertainty paradigm are outlined. Finally, several discrete,
continuous and hybrid numerical examples including comparisons illustrate the
effectiveness of the theoretical results.Comment: 21 pages, 8 figure
Communication Subsystems for Emerging Wireless Technologies
The paper describes a multi-disciplinary design of modern communication systems. The design starts with the analysis of a system in order to define requirements on its individual components. The design exploits proper models of communication channels to adapt the systems to expected transmission conditions. Input filtering of signals both in the frequency domain and in the spatial domain is ensured by a properly designed antenna. Further signal processing (amplification and further filtering) is done by electronics circuits. Finally, signal processing techniques are applied to yield information about current properties of frequency spectrum and to distribute the transmission over free subcarrier channels
- …