636 research outputs found
Time-frequency analysis of signals using support adaptive Hermite-Gaussian expansions
Cataloged from PDF version of article.Since Hermite–Gaussian (HG) functions provide an orthonormal basis with the most compact time–
frequency supports (TFSs), they are ideally suited for time–frequency component analysis of finite energy
signals. For a signal component whose TFS tightly fits into a circular region around the origin, HG
function expansion provides optimal representation by using the fewest number of basis functions.
However, for signal components whose TFS has a non-circular shape away from the origin, straight
forward expansions require excessively large number of HGs resulting to noise fitting. Furthermore, for
closely spaced signal components with non-circular TFSs, direct application of HG expansion cannot
provide reliable estimates to the individual signal components. To alleviate these problems, by using
expectation maximization (EM) iterations, we propose a fully automated pre-processing technique which
identifies and transforms TFSs of individual signal components to circular regions centered around the
origin so that reliable signal estimates for the signal components can be obtained. The HG expansion
order for each signal component is determined by using a robust estimation technique. Then, the
estimated components are post-processed to transform their TFSs back to their original positions.
The proposed technique can be used to analyze signals with overlapping components as long as the
overlapped supports of the components have an area smaller than the effective support of a Gaussian
atom which has the smallest time-bandwidth product. It is shown that if the area of the overlap
region is larger than this threshold, the components cannot be uniquely identified. Obtained results on
the synthetic and real signals demonstrate the effectiveness for the proposed time–frequency analysis
technique under severe noise cases.
© 2012 Elsevier Inc. All rights reserved
High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: Sampling Cost via Incident-Field Windowing and Recentering
This paper proposes a frequency/time hybrid integral-equation method for the
time dependent wave equation in two and three-dimensional spatial domains.
Relying on Fourier Transformation in time, the method utilizes a fixed
(time-independent) number of frequency-domain integral-equation solutions to
evaluate, with superalgebraically-small errors, time domain solutions for
arbitrarily long times. The approach relies on two main elements, namely, 1) A
smooth time-windowing methodology that enables accurate band-limited
representations for arbitrarily-long time signals, and 2) A novel Fourier
transform approach which, in a time-parallel manner and without causing
spurious periodicity effects, delivers numerically dispersionless
spectrally-accurate solutions. A similar hybrid technique can be obtained on
the basis of Laplace transforms instead of Fourier transforms, but we do not
consider the Laplace-based method in the present contribution. The algorithm
can handle dispersive media, it can tackle complex physical structures, it
enables parallelization in time in a straightforward manner, and it allows for
time leaping---that is, solution sampling at any given time at
-bounded sampling cost, for arbitrarily large values of ,
and without requirement of evaluation of the solution at intermediate times.
The proposed frequency-time hybridization strategy, which generalizes to any
linear partial differential equation in the time domain for which
frequency-domain solutions can be obtained (including e.g. the time-domain
Maxwell equations), and which is applicable in a wide range of scientific and
engineering contexts, provides significant advantages over other available
alternatives such as volumetric discretization, time-domain integral equations,
and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now
including direct comparisons to existing CQ and TDIE solver implementations)
(Part I of II
Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos
Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the nonintrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method. Compared with the popular intrusive stochastic Galerkin (SG) method, the coupled deterministic equations resulting from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST requires fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems
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