Search results for "transforms"
showing 10 items of 40 documents
Measuring spectrally-resolved information transfer.
2020
Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in t…
A low cost and easy re-configurable instrument for power quality survey
2004
In this document the development of a low cost and user friendly PC-based instrument for power quality measurement is proposed, according to IEC 61000-4-7 and standard IEC 61000-4-30. It is an easily re-configurable instrument able to measure harmonics, interharmonics and amplitude disturbances and supply unbalance. In order to verify its accuracy, the instrument has been tested according standard test procedures, by means of a built-up calibration test bench.
Improved Statistically Based Retrievals via Spatial-Spectral Data Compression for IASI Data
2019
In this paper, we analyze the effect of spatial and spectral compression on the performance of statistically based retrieval. Although the quality of the information is not com- pletely preserved during the coding process, experiments reveal that a certain amount of compression may yield a positive impact on the accuracy of retrievals. We unveil two strategies, both with interesting benefits: either to apply a very high compression, which still maintains the same retrieval performance as that obtained for uncompressed data; or to apply a moderate to high compression, which improves the performance. As a second contribution of this paper, we focus on the origins of these benefits. On the one…
Additive properties of fractal sets on the parabola
2023
Let $0 \leq s \leq 1$, and let $\mathbb{P} := \{(t,t^{2}) \in \mathbb{R}^{2} : t \in [-1,1]\}$. If $K \subset \mathbb{P}$ is a closed set with $\dim_{\mathrm{H}} K = s$, it is not hard to see that $\dim_{\mathrm{H}} (K + K) \geq 2s$. The main corollary of the paper states that if $0 0$. This information is deduced from an $L^{6}$ bound for the Fourier transforms of Frostman measures on $\mathbb{P}$. If $0 0$, then there exists $\epsilon = \epsilon(s) > 0$ such that $$ \|\hat{\mu}\|_{L^{6}(B(R))}^{6} \leq R^{2 - (2s + \epsilon)} $$ for all sufficiently large $R \geq 1$. The proof is based on a reduction to a $\delta$-discretised point-circle incidence problem, and eventually to the $(s,2s)$-…
Comparison of two different approaches for harmonic distortion sources assessment
2021
The paper focuses the attention on the comparison of two approaches for power quality assessment in the electric grid. Both approaches are suitable for investigating the harmonic pollution source and discovering if the harmonic source comes from the customer or the utility grid. The two approaches have the same purpose but they are deeply different. The first approach is based on the knowledge of the customer and utility equivalent impedance while the second is based on single point measurement at point of common coupling PCC. In this paper, the advantages and drawbacks of the two approaches are investigated also supported by a case study.
A PC-based instrument for harmonics and interharmonics measurement in power supply systems
2004
Abstract Growing interest on power quality has led international working groups to define new standards for testing and measurement techniques to apply to power systems. Special attention has been paid to harmonic and interharmonic measurements. Here, the authors introduce a PC-based instrument capable of synchronising sampling frequency with fundamental frequency in order to perform on-line voltage or current distortion analysis. The instrument has been developed in accordance with currently available standards and international documents, IEC 61000-4-7 Ed. 2002, IEC 61000-4-30 Ed. 2003, Draft Guide IEEE P1159.1 Ed. 2003 and limits given by IEC 61000 Part. 3. A detailed description of the …
Complex singularities and PDEs
2015
In this paper we give a review on the computational methods used to capture and characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the classical singularity tracking method and give an example of application using the Burgers equation as a case study. This method is based on the analysis of the Fourier spectrum of the solution and it allows to determine and characterize the complex singularity closest to the real domain. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Padé approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the s…
FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS
2020
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set, $\Sc'(\mathbb R)$, the set of tempered distributions, provided they satisfy some mild conditions. We discuss some examples, and we show how our definition can be used in a quantum mechanical context.
An Advanced Numerical Model in Solving Thin-Wire Integral Equations by Using Semi-Orthogonal Compactly Supported Spline Wavelets
2003
Abstract—In this paper, the semi-orthogonal compactly sup- ported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computation- ally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze elec…
Statistical atmospheric parameter retrieval largely benefits from spatial-spectral image compression
2021
The infrared atmospheric sounding interferometer (IASI) is flying on board of the Metop satellite series, which is part of the EUMETSAT Polar System. Products obtained from IASI data represent a significant improvement in the accuracy and quality of the measurements used for meteorological models. Notably, the IASI collects rich spectral information to derive temperature and moisture profiles, among other relevant trace gases, essential for atmospheric forecasts and for the understanding of weather. Here, we investigate the impact of near-lossless and lossy compression on IASI L1C data when statistical retrieval algorithms are later applied. We search for those compression ratios that yield…