Search results for "Fourier Analysis"
showing 10 items of 113 documents
Measuring guided waves in long bones: Modeling and experiments in free and immersed plates
2005
Guided waves, consistent with the A0 Lamb mode, have previously been observed in bone phantoms and human long bones. Reported velocity measurements relied on line fitting of the observed wave fronts. Such an approach has limited ability to assess dispersion and is affected by interference by other wave modes. For a more robust identification of modes and determination of phase velocities, signal processing techniques using the fast Fourier transform (FFT) were investigated. The limitations of FFT because of spatial resolution were addressed to improve the precision of the measured modes. An inversion scheme was developed for determining the plate thickness from the measured velocity. Experi…
Ferroelectric Behavior in Epitaxial Films of Relaxor PbMg1/3Nb2/3O3
2004
The nonlinear dielectric response of epitaxial thin films of relaxor ferroelectric PbMg1/3Nb2/3O3 was experimentally studied using digital Fourier analysis. Change from glass-like to ferroelectric behavior was detected in a broad temperature range, at relatively low ac and/or dc electric fields, and at a time scale of seconds. The presence of interfaces and peculiar microstructure of thin films are suggested to determine such a specific behavior.
The effects of linearly increasing flip angles on 3D inflow MR angiography
1994
As recently demonstrated, spin saturation effects in 3D time-of-flight (TOF) MR angiography (MRA) can be reduced by using RF pulses with linearly increasing flip angles (ramp pulses) in the main direction of flow. We developed a model for calculating the signal distribution of proton flow within the excitation volume (slab) for different ramp slopes and compared the results with the measured distribution for the lower-leg arteries. The ramp pulses were generated using the Fourier transformation of the desired excitation profiles. With a bandwidth of 6 kHz and a pulse length of 2.56 ms satisfactory ramps with variable slopes were generated and applied in a standard flow-compensated 3D FISP s…
A NEW REPRESENTATION OF ENERGY STORAGE SYSTEMS OPERATION USING FOURIER THEORY IN OPTIMAL SMART GRIDS MANAGEMENT
2012
This paper investigates the possibility to use a new modeling of Energy Storage Systems based on zero integral functions. Such functions represent the course of the energy level stored in batteries during the solution of optimal management problems in smart-grids. Storage devices, such as all the other components that are required to meet an integral capacity constraint along the dispatch time, must show the same State of Charge at the start and at the end of the timeframe considered for operation. In this paper, a set of sinusoidal functions have been used for the synthesis of the charge and discharge course of energy Storage Systems. Such representation allows to eliminate the difficult c…
Using Fourier local magnitude in adaptive smoothness constraints in motion estimation
2007
Like many problems in image analysis, motion estimation is an ill-posed one, since the available data do not always sufficiently constrain the solution. It is therefore necessary to regularize the solution by imposing a smoothness constraint. One of the main difficulties while estimating motion is to preserve the discontinuities of the motion field. In this paper, we address this problem by integrating the motion magnitude information obtained by the Fourier analysis into the smoothness constraint, resulting in an adaptive smoothness. We describe how to achieve this with two different motion estimation approaches: the Horn and Schunck method and the Markov Random Field (MRF) modeling. The t…
Parametric and nonparametric methods to generate time-varying surrogate data.
2009
We present both nonparametric and parametric approaches to generating time-varying surrogate data. Nonparametric and parametric approaches are based on the use of the short-time Fourier transform and a time-varying autoregressive model, respectively. Time-varying surrogate data (TVSD) can be used to determine the statistical significance of the linear and nonlinear coherence function estimates. Two advantages of the TVSD are that it keeps one from having to make an arbitrary decision about the significance of the coherence value, and it properly takes into account statistical significance levels, which may change with time. Our simulation examples and experimental results on blood pressure …
On Radon Transforms on Tori
2014
We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere. We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients. These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.
Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below
2013
We prove existence and uniqueness of optimal maps on $RCD^*(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.
On Radon transforms on compact Lie groups
2016
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from $S^1$.
Notes on bilinear multipliers on Orlicz spaces
2019
Let $\Phi_1 , \Phi_2 $ and $ \Phi_3$ be Young functions and let $L^{\Phi_1}(\mathbb{R})$, $L^{\Phi_2}(\mathbb{R})$ and $L^{\Phi_3}(\mathbb{R})$ be the corresponding Orlicz spaces. We say that a function $m(\xi,\eta)$ defined on $\mathbb{R}\times \mathbb{R}$ is a bilinear multiplier of type $(\Phi_1,\Phi_2,\Phi_3)$ if \[ B_m(f,g)(x)=\int_\mathbb{R} \int_\mathbb{R} \hat{f}(\xi) \hat{g}(\eta)m(\xi,\eta)e^{2\pi i (\xi+\eta) x}d\xi d\eta \] defines a bounded bilinear operator from $L^{\Phi_1}(\mathbb{R}) \times L^{\Phi_2}(\mathbb{R})$ to $L^{\Phi_3}(\mathbb{R})$. We denote by $BM_{(\Phi_1,\Phi_2,\Phi_3)}(\mathbb{R})$ the space of all bilinear multipliers of type $(\Phi_1,\Phi_2,\Phi_3)$ and inve…