7,372 research outputs found
A FRACTIONAL DELAY FIR FILTER BASED ON LAGRANGE INTERPOLATION OF FARROW STRUCTURE
An efficient implementation technique for the Lagrange interpolation is derived. This formulation called the Farrow structure leads to a version of Lagrange interpolation that is well suited to time varying FD filtering. Lagrange interpolation is mostly used for fractional delay approximation as it can be used for increasing the sampling rate of signals and systems. Lagrange interpolation is one of the representatives for a class of polynomial interpolation techniques. The computational cost of this structure is reduced as the number of multiplications are minimised in the new structure when compared with the conventional structure
Spectral filtering for the reduction of the Gibbs phenomenon of polynomial approximation methods on Lissajous curves with applications in MPI
Polynomial interpolation and approximation methods on sampling points along Lissajous curves using Chebyshev series is an effective way for a fast image reconstruction in Magnetic Particle Imaging. Due to the nature of spectral methods, a Gibbs phenomenon occurs in the reconstructed image if the underlying function has discontinuities. A possible solution for this problem are spectral filtering methods acting on the coefficients of the approximating polynomial. In this work, after a description of the Gibbs phenomenon and classical filtering techniques in one and several dimensions, we present an adaptive spectral filtering process for the resolution of this phenomenon and for an improved approximation of the underlying function or image. In this adaptive filtering technique, the spectral filter depends on the distance of a spatial point to the nearest discontinuity. We show the effectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers
We propose a solution strategy for a multimaterial minimum compliance
topology optimization problem, which consists in finding the optimal allocation
of a finite number of candidate (possibly anisotropic) materials inside a
reference domain, with the aim of maximizing the stiffness of the body. As a
relevant and novel application we consider the optimization of self-assembled
structures obtained by means of diblock copolymers. Such polymers are a class
of self-assembling materials which spontaneously synthesize periodic
microstructures at the nanoscale, whose anisotropic features can be exploited
to build structures with optimal elastic response, resembling biological
tissues exhibiting microstructures, such as bones and wood. For this purpose we
present a new generalization of the classical Optimality Criteria algorithm to
encompass a wider class of problems, where multiple candidate materials are
considered, the orientation of the anisotropic materials is optimized, and the
elastic properties of the materials are assumed to depend on a scalar
parameter, which is optimized simultaneously to the material allocation and
orientation. Well-posedness of the optimization problem and well-definition of
the presented algorithm are narrowly treated and proved. The capabilities of
the proposed method are assessed through several numerical tests
A new generation 99 line Matlab code for compliance Topology Optimization and its extension to 3D
Compact and efficient Matlab implementations of compliance Topology
Optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125
lines respectively. On discretizations ranging from to
elements, the 2D version, named top99neo, shows speedups from
2.55 to 5.5 times compared to the well-known top88 code (Andreassen-etal 2011).
The 3D version, named top3D125, is the most compact and efficient Matlab
implementation for 3D TO to date, showing a speedup of 1.9 times compared to
the code of Amir-etal 2014, on a discretization with elements.
For both codes, improvements are due to much more efficient procedures for the
assembly and implementation of filters and shortcuts in the design update step.
The use of an acceleration strategy, yielding major cuts in the overall
computational time, is also discussed, stressing its easy integration within
the basic codes.Comment: 17 pages, 8 Figures, 4 Table
Fractionally-addressed delay lines
While traditional implementations of variable-length digital delay lines are
based on a circular buffer accessed by two pointers, we propose an
implementation where a single fractional pointer is used both for read and
write operations. On modern general-purpose architectures, the proposed method
is nearly as efficient as the popularinterpolated circular buffer, and it
behaves well for delay-length modulations commonly found in digital audio
effects. The physical interpretation of the new implementation shows that it is
suitable for simulating tension or density modulations in wave-propagating
media.Comment: 11 pages, 19 figures, to be published in IEEE Transactions on Speech
and Audio Processing Corrected ACM-clas
Efficient Linear Programming for Dense CRFs
The fully connected conditional random field (CRF) with Gaussian pairwise
potentials has proven popular and effective for multi-class semantic
segmentation. While the energy of a dense CRF can be minimized accurately using
a linear programming (LP) relaxation, the state-of-the-art algorithm is too
slow to be useful in practice. To alleviate this deficiency, we introduce an
efficient LP minimization algorithm for dense CRFs. To this end, we develop a
proximal minimization framework, where the dual of each proximal problem is
optimized via block coordinate descent. We show that each block of variables
can be efficiently optimized. Specifically, for one block, the problem
decomposes into significantly smaller subproblems, each of which is defined
over a single pixel. For the other block, the problem is optimized via
conditional gradient descent. This has two advantages: 1) the conditional
gradient can be computed in a time linear in the number of pixels and labels;
and 2) the optimal step size can be computed analytically. Our experiments on
standard datasets provide compelling evidence that our approach outperforms all
existing baselines including the previous LP based approach for dense CRFs.Comment: 24 pages, 10 figures and 4 table
Variable-rate data sampling for low-power microsystems using modified Adams methods
A method for variable-rate data sampling is proposed for the purpose of low-power data acquisition in a small footprint microsystem. The procedure enables energy saving by utilizing dynamic power management techniques and is based on the Adams-Bashforth and Adams-Moulton multistep predictor-corrector methods for ordinary differential equations. Newton-Gregory backward difference interpolation formulae and past value substitution are used to facilitate sample rate changes. It is necessary to store only 2m+1 equispaced past values of t and the corresponding values of y, where y=g(t), and m is the number of steps in the Adams methods. For the purposes of demonstrating the technique, fourth-order methods are used, but it is possible to use higher orders to improve accuracy if required
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