Search results for "Fourier transforms"
showing 7 items of 7 documents
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.
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 $(s,2s)$-…
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.
On a Continuous Sárközy-Type Problem
2022
Abstract We prove that there exists a constant $\epsilon> 0$ with the following property: if $K \subset {\mathbb {R}}^2$ is a compact set that contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\dim _{\textrm {H}} K \leq 2 - \epsilon $.
Vibration signature analysis for monitoring rotor broken bar in double squirrel cage induction motors based on wavelet analysis
2014
Purpose – The purpose of this paper is to present a diagnosis technique, for rotor broken bar in double cage induction motor, based on advanced use of wavelet transform analysis. The proposed technique is experimentally validated. Design/methodology/approach – The proposed approach is based on a combined use of frequency sliding and wavelet transform analysis, to isolate the contribution of the rotor fault components issued from vibration signals in a single frequency band. Findings – The proposed technique is reliable for tracking the rotor fault components over time-frequency domain. The quantitative analysis results based on this technique are the proof of its robustness. Research limit…