Search results for "transforms"
showing 10 items of 40 documents
Fractional Derivatives in Interval Analysis
2017
In this paper, interval fractional derivatives are presented. We consider uncertainty in both the order and the argument of the fractional operator. The approach proposed takes advantage of the property of Fourier and Laplace transforms with respect to the translation operator, in order to first define integral transform of interval functions. Subsequently, the main interval fractional integrals and derivatives, such as the Riemann–Liouville, Caputo, and Riesz, are defined based on their properties with respect to integral transforms. Moreover, uncertain-but-bounded linear fractional dynamical systems, relevant in modeling fractional viscoelasticity, excited by zero-mean stationary Gaussian…
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…
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…
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 …
Diagnosis of mechanical unbalance for double cage induction motor load in time-varying conditions based on motor vibration signature analysis
2013
This paper investigates the detectability of mechanical unbalance in double cage induction motor load using motor vibration signature analysis technique. Rotor imbalances induce specific harmonic components in electrical, electromagnetical, and mechanical quantities. Harmonic components characteristic of this category of rotor faults, issued from vibration signals analysis, are closely related to rotating speed of the rotor, which complicates its detection under non-stationary operating conditions of the motor. Firstly, experimental results were performed first under healthy and mechanical load unbalance cases, for different load levels under steady-state operating conditions to evaluate th…
A robust blind 3-D mesh watermarking based on wavelet transform for copyright protection
2019
Nowadays, three-dimensional meshes have been extensively used in several applications such as, industrial, medical, computer-aided design (CAD) and entertainment due to the processing capability improvement of computers and the development of the network infrastructure. Unfortunately, like digital images and videos, 3-D meshes can be easily modified, duplicated and redistributed by unauthorized users. Digital watermarking came up while trying to solve this problem. In this paper, we propose a blind robust watermarking scheme for three-dimensional semiregular meshes for Copyright protection. The watermark is embedded by modifying the norm of the wavelet coefficient vectors associated with th…
Coherent Quantum Tomography
2016
We discuss a quantum mechanical indirect measurement method to recover a position dependent Hamilton matrix from time evolution of coherent quantum mechanical states through an object. A mathematical formulation of this inverse problem leads to weighted X-ray transforms where the weight is a matrix. We show that such X-ray transforms are injective with very rough weights. Consequently, we can solve our quantum mechanical inverse problem in several settings, but many physically relevant problems we pose also remain open. We discuss the physical background of the proposed imaging method in detail. We give a rigorous mathematical treatment of a neutrino tomography method that has been previous…
The Study of Dynamic Objects Identification Algorithms Based on Anisotropic Properties of Generalized Amplitude-Phase Images
2018
The article presents some results of dynamical objects identification technology based on coincidence matrixes of templates and tested objects’ amplitude-phase images (APIm) calculated with discrete Hilbert transforms (DHT). DHT algorithms are modeled on basis of isotropic (HTI), anisotropic (HTA), generalized transforms – AP-analysis (APA) and the difference (residual) relative shifted phase (DRSP-) images to calculate the APIm. The identified objects are recognized as members of classes modeled with 3D templates – images of different types airplanes rotated in space. The dynamic anisotropic properties of APIm causes the increasing of sensitivity to circular angle rotation and make possibl…
Radon transform as a set of probability distributions
2009
It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.
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 $(s,2s)$-…