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# Harmonic Analysis - Science topic

Ths group is devoted to Harmonic Analysis (Fourier Analysis, Time Frequency A., Gabor Analysis...)
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Publications related to Harmonic Analysis (10,000)
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Multiphase drives exhibit remarkable advantages (e.g., fault tolerance) over three-phase ones. Six-phase drives are particularly attractive, given their moderate complexity and suitability for off-the-shelf three-phase converters. Regarding the stator winding arrangement, the symmetrical one offers superior postfault capabilities in most scenarios....
Article
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Dual three-phase permanent magnet synchronous machines (DTP-PMSMs) are famous for their fault-tolerant capability. However, the complex modeling, high copper loss and torque ripple under post-fault operation limit their further application. In this paper, a fault tolerant control (FTC) strategy is developed for DTP-PMSMs under the open-phase fault...
Article
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Previous studies have demonstrated that tides are subject to considerable changes on secular time scales. However, these studies rely on sea level observations from tide gauges that are predominantly located in coastal and shelf regions and therefore, the large‐scale patterns remain uncertain. Now, for the first time, satellite radar altimetry (TOP...
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Induction motors are susceptible to many types of faults that can become catastrophic and cause production stoppages. To predict emerging faults and avoid an unexpected failure, an induction motor can be diagnosed using the proposed motor current normalized residual harmonic analysis method. This method is simple and efficient. It is based on a mor...
Article
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Tidal water levels and currents in the shallow water environments of the inner shelf are subject to nonlinear interactions that produce higher frequency harmonics known as overtides, which contribute to the residual transport of scalars. The primary hydrodynamic overtide generating mechanisms (advection, nonlinear continuity and bottom friction) ar...
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Tchaikovsky is known as the “master of melody.” His melodies are extremely rich, and he is good at using small musical forms to express rich and deep emotional feelings. The musical form and structure of “June: Barcarolle” in Tchaikovsky’s piano collection “The Seasons” will be discussed in this paper.
Article
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Multiphase winding configurations have gained significant attention in high-performance variable speed drives and wind energy conversion systems (WECS) owing to their myriad advantages. In the available literature, various multiphase winding layouts have been designed aiming at boosting the machine performance to meet the requirements of the propos...
Article
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Wavelet transform is a powerful tool for analysing the problems arising in harmonic analysis, signal and image processing, sampling, filtering, and so on. However, they seem to be inadequate for representing those signals whose energy is not well concentrated in the frequency domain. In pursuit of representations of such signals, we propose a novel...
Presentation
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These are the slides of a talk given at the conference held in Bedlewo, Sept. 12-16, 2022. The conference has been organised by Kenny De Commer, Adam Skalski, Johan Konings, Jacek Krajczok. The conference was titled Noncommutative Harmonic Analysis and Quantum Groups. Huang posed the problem of giving a direct proof of a theorem of Finkelberg regar...
Article
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Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored. Here, we present a description of the prime spectrum of this ring and study some of the algebraic and topological properties of these prime ideals. We also study h...
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The recent emergence of magnetic van der Waals materials allows for the investigation of current-induced magnetisation manipulation in two-dimensional materials. Uniquely, Fe3GeTe2 has a crystalline structure that allows for the presence of bulk spin–orbit torques (SOTs) that we quantify in a Fe3GeTe2 flake. From the symmetry of the measured torque...
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Source-grid-load-storage has represented an interactive characteristic in the active distribution network (ADN). Moreover, power electronic devices have been widely used for source-grid-load-storage with the rapid development of power electronics technology. In this condition, the large-scale distributed source may cause voltage quality degradation...
Preprint
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We give a free probabilistic proposal to compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model where the gravitational path integral can be implemented with full control. We observe that the replica trick gravitational path integral is combinatorially mat...
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We introduce a fully informative distribution network phasor measurement unit (FI-DPMU), that is capable of performing a simultaneous estimation of phasor dynamics and harmonic components. This is in contrast with current state-of-the-art devices, that only provide information about the fundamental component of voltages/currents—by discriminating o...
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Deep brain stimulation (DBS) therapies have shown clinical success in the treatment of a number of neurological illnesses, including obsessive-compulsive disorder, epilepsy, and Parkinson’s disease. An emerging strategy for increasing the efficacy of DBS therapies is to develop closed-loop, adaptive DBS systems that can sense biomarkers associated...
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The Dirac-Dolbeault operator for a compact oriented Kähler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a manifold with boundary allows to express the values of the sections of the Dirac bundle in terms of the values on the boundary, extending the mean value theorem of harmonic analysis. Utilizing...
Preprint
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We provide a convenient framework for the study of the well-posedness of a variety of abstract (integro)differential equations in general Banach function spaces. It allows us to extend and complement the known theory on the maximal regularity of such equations. More precisely, by methods of harmonic analysis, we identify large classes of Banach spa...
Preprint
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Herz spaces with special exponents initially appeared in the work of C. S. Herz on mapping properties of Fourier transform on a Lipschitz class. After S. Lu and D. Yang introduced these spaces with general indices, they have gained a considerable interest in harmonic analysis. The purpose of this paper is to study a Lorentz space variant of the cla...
Article
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This paper uses some basic notions and results from the discrete harmonic analysis associated with the Jacobi–Dunkl operator to study some problems in the theory of approximation of functions in the space $$\mathbb {L}_{2}^{(\alpha ,\beta )}$$. Analogs of the direct Jackson theorems of approximations for the modulus of smoothness (of arbitrary or...
Conference Paper
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By clicking on [submit] you agree with the »privacy-policy. Type: poster Abstract: Seismological data analysis is done by wavelet transform-spectral decomposition,singular spectrum analysis, nonlinear nonstationary signal processing by empirical mode decomposition Hilbert Huang transform,etc. Wavelet transform suffers from spectral leakage smearing...
Presentation
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The theme of the talk originates at the borderline between the classical Hardy--Littlewood--Winer Maximal and the Hardy--Littlewood--Sobolev Fractional Integral Theorems, two results that, for quite a while, guided the development of Euclidean harmonic analysis. The first part of the talk introduces a Linking Up Lemma stated in a measure space sett...
Conference Paper
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Sea level that deviates from the geoid represents dynamic topography, whereas the mean dynamic topography (MDT) represents the ocean circulation, which over different time scale can reveal the persistent or semi-persistent dynamics pattern characteristics. Determination of MDT is performed by the oceanography approach (utilizing hydrodynamic models...
Article
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There are several proofs by now for the famous Cwikel–Lieb–Rozenblum (CLR) bound, which is a semiclassical bound on the number of bound states for a Schrödinger operator, proven in the 1970s. Of the rather distinct proofs by Cwikel, Lieb, and Rozenblum, the one by Lieb gives the best constant, the one by Rozenblum does not seem to yield any reasona...
Article
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This article documents the design, manufacture, and testing of a silicon inertial optical sensor for low-frequency (lower than 2 kHz) applications. Three accelerometer designs optimized by parameterization using Finite Element Analysis were considered. The accelerometers were manufactured and the one with the highest performance at low frequency wa...
Article
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Northern Hemisphere planetary waves exhibit an abrupt change in early summer and a significant impact on East Asian summer monsoon rainfall. Although great achievements have been made toward understanding the characteristics and maintenance of planetary waves during winter and summer, the transition of planetary waves during the abrupt-change perio...
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Recently, the authors have introduced and intensively studied a class of bounded Hilbert space operators called conditionally positive definite. Its origins go back to the harmonic analysis on ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
Article
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In harmonic gyrotrons, the narrow operating region of the harmonic mode is significantly restricted by the severe mode competition from the fundamental parasitic modes, which makes it important to study the nonlinear effects of beam-wave interaction in the case of a nonideal electron beam. In this article, the effect of the electron velocity spread...
Preprint
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Harmonic analysis of time series from 20 years of MODIS-Aqua ocean color observations (2002–2022) is conducted to identify periodic variability of near-surface chlorophyll (Chl-a) inferred from ocean color. As they are based on satellite imagery, the Chl-a observations are characterized by significant gaps in both spatial and temporal coverage due...
Preprint
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Motivated by the subjective definition of abstraction provided in (Gilead, Trope, & Liberman, 2020), we illustrate here a universal abstraction process relying on Naive Set Theory. This concept, originating with the work of Dedekind, Frege, and Cantor in the second half of the nineteenth century, has been formalized in mathematics for some time and...
Article
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Motivated by the results from the classical probability theory, we introduce the concepts of tangency and weak domination of noncommutative martingales. Then we establish the weak-type and strong-type estimates arising in this context. The proof rests on a novel Gundy-type decomposition which is of independent interest. We also show the correspondi...
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This paper uses some basic concepts and results on harmonic analysis associated with Heckman-Opdam theory on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {... Preprint Full-text available In this paper, we prove weighted versions of the Gagliardo-Nirenberg interpolation inequality with Riesz as well as Bessel type fractional derivatives. We use a harmonic analysis approach employing several methods, including the method of domination by sparse operators, to obtain such inequalities for a general class of weights satisfying Muckenhou... Article Full-text available The purpose of this study was to evaluate corneal irregular astigmatism of patients with granular and lattice corneal dystrophy (GCD and LCD). 70 GCD, 35 LCD, and 81 control eyes were included. Anterior and posterior corneal topographic data obtained from anterior segment optical coherence tomography were expanded into four components via Fourier h... Article Full-text available The analysis of harmonics and non-sinusoidal waveform shape in time-series data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a wel... Preprint Full-text available The ocean occupies 70% of the world's surface area, and extreme changes in sea level can have an even greater impact on humans. Therefore, it is necessary to make an accurate advance prediction of extreme sea level. In this paper, a model with robustness, high accuracy and universal applicability has been constructed based on Nonlinear Auto-Regress... Preprint Full-text available The northern Gulf of Mexico coast is affected by the North Atlantic hurricane season, which brings serious economic losses to the southern U.S. every year; therefore, it is necessary to make an accurate advance prediction of storm surge level. In this paper, a prediction model has been constructed based on Nonlinear Auto-Regressive Exogenous (NARX)... Conference Paper Full-text available The Concept of DGs is developed to utilize the small scale renewable energy resources to meet the local power demand and microgrids are getting importance as they allow the penetration of DGs. Microgrid should be operated in an islanded mode to increase supply reliability. To operate a microgrid in islanded mode, there are two major issues to be ad... Preprint Full-text available Optical second harmonic generation is a second-order nonlinear process by which two photons of a given frequency can combine in a nonlinear medium to generate a third photon at twice the frequency. Since the electric-dipole SHG process only occurs in non-centrosymmetric crystals, it is widely used as a sensitive probe to detect broken inversion sym... Article Full-text available Wireless uplink of a sensor node based on modulating rectifier-generated harmonics is promising for lowered energy consumption and Tx-to-Rx leakage. The existing solutions need to balance between maintaining the rectification performance and modulating the reradiated harmonic. In this article, a novel controllable second-harmonic termination (CSHT)... Article Full-text available Electrical impedance tomography (EIT) has the potential for monitoring perfusion in addition to respiration on the bedside. Several separation methods were reported, e.g. Filtering, ECG-gating and PCA. However, the separation is not trivial, which is why harmonic analysis was introduced in EIT data analysis. It is based on several assumptions and t... Article Full-text available In this study, the change in the electrical performance of epoxy/MgO, which is one of the materials used to increase the performance of epoxy resin, was evaluated under the effect of water. Accordingly, comparative tracking index (CTI) experiments, which are one of the effective methods used to model electricity's effect on surface properties, were... Article Full-text available Pseudorandom sequences, sometimes shortened as sequences, have played a key role in the applications of digital communications, cryptography and computer science. This research field is an example of scientific research directly born from the real world applications. Specifically, the research on sequences stems from the application of the sequence... Article Full-text available High Impedance Fault (HIF) is a problematic fault of feeders which its fault current is lower as compared to normal current in power system. Likewise, due to magnitude of impedance engaged in fault area and behavior of fault current is specific and not the same as the usual fault current profile which cannot be identified by standard relays. The HI... Article Full-text available Contact problems with Coulomb friction in linear elasticity are notoriously difficult, and their mathematical analysis is still largely incomplete. In this paper, a model problem with heterogeneous friction coefficient is considered in two-dimensional elasticity. For this model problem, an existence and uniqueness result is proved, relying heavily... Article Full-text available The hydrodynamic effects of the largest suspended mussel farms in the East China Sea near Gouqi Island, was investigated using a high-resolution 3D ocean model and field observations. To capture the 3D farm effects on hydrodynamics, an additional depth dependent momentum sink term was introduced in the model. The model results compared well with th... Article Full-text available In this paper, we introduce the k-generalized Stockwell transform on R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document}. We investigate for... Article Full-text available Contact of materials is inevitable in machine environment where a number of elements interact with each other causing impact force and consequent stress and strain at point of contact. The study of this behaviour is essential for machine design applications as it helps to predict life of a particular element as per the amount of stress it can susta... Article Full-text available Remote Sensing Ecological Index (RSEI) is one of the most widely used ecological quality assessment indicators. Due to the noise caused by adverse atmoshperic conditions and other factors, the RSEI calculated from the original image usually has the phenomena of lack of information and unstable image quality. Therefore, based on Google Earth Engine... Article Full-text available In this paper we obtain quantitative weighted$$L^p$$L p -inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain$$L^p(w)$$L p ( w ) -operator norms in terms of the$$A_p A p -characteristic of the weight w . In order to do this we show that t...
Article
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With the increasing integration of new technologies, power system operators are facing new operational and planning challenges. Most of these changes are caused by power electronics devices of low carbon (LC) units, resulting in more frequent violations of limits defined in the standards, such as the unwanted occurrence of higher-order harmonics. T...
Article
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Heat transport through short and closed vegetation such as grass is modelled by a simple diffusion process. The grass is treated as a homogeneous ‘sponge layer’ with uniform thermal diffusivity and conductivity, placed on top of the soil. The temperature and heat-flux dynamics in both vegetation and soil are described using harmonic analysis. All t...
Article
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Multiphase electric drives offer attractive advantages over conventional three-phase systems. Some of the benefits are shared by all multiphase configurations, but the performance can be highly affected by the specific location of the stator windings. While the asymmetrical configuration has been traditionally a popular choice, the symmetrical disp...
Article
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Understanding nodal tidal characteristics is essential for accurate long-term tidal prediction. Observational nodal evolution of tides is mainly based on tide gauge records in coastal areas which are limited in time and space, thus impeding coherent determinations of basin-wide patterns of tidal variability. In this paper, we indicate the potential...
Article
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Spaceborne Synthetic Aperture Radar (SAR) are well-established systems for flood mapping, thanks to their high sensitivity towards water surfaces and their independence from daylight and cloud cover. Particularly able is the 2014-launched Copernicus Sentinel-1 C-band SAR mission, with its systematic monitoring schedule featuring global land coverag...
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The photoplethysmographic (PPG) waveform contains hemodynamic information in its oscillations. We provide a new method for quantitative study of the waveform morphology and its relationship to the hemodynamics. A data adaptive modeling of the waveform shape is used to describe the PPG waveforms recorded from ear and finger. Several indices, based o...
Article
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Due to the conservation of global angular momentum, polar motion (PM) is dominated by global mass redistributions and relative motions in the atmosphere, oceans and land water at seasonal time scales. Thus, accurately measured PM data can be used to validate the general circulation models (GCMs) for the atmosphere, oceans and land water. This study...
Article
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Thanks to the recent development of sensors and Internet of Things (IoT), it is now common to use mobile application to monitor health status. These applications rely on sensors embedded in the smartphones that measure several physical quantities such as acceleration or angular velocity. However, these data are private information that can be used...
Article
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The shoot-through (ST) states are essential for the operation of sinusoidal pulse-width-modulation (SPWM) based Z-source inverters. However, the insertion of shoot-through state unavoidably leads to output harmonics which is greatly affected by its distribution, especially for bipolar modulation schemes. With quantitative analysis, this paper inves...
Preprint
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We investigate strongly symmetric homeomorphisms of the real line which appear in harmonic analysis aspects of quasiconformal Teichm\"uller theory. An element in this class can be characterized by a property that it can be extended quasiconformally to the upper half-plane so that its complex dilatation induces a vanishing Carleson measure. However,...
Article
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This paper presents a novel 400 V–50 V bidirectional DHC-LT resonant DC-DC converter. By adding a resonant capacitor and an auxiliary transformer based on LLC, zero-voltage switching (ZVS) and zero-current switching (ZCS) are achieved, while the output voltage gain range is broadened in two directions. Operation principles and robustness are discus...
Article
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This research article is enriched with the mechanical behavior of an electro-mechanical system (EMS) for robotics. An electrically powered system is modelled and tested under vibration and heat flow conditions. The vibration analyses are carried out in the aspects of model and harmonic. The natural frequency and the amplitude of vibration are predi...
Preprint
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In this paper, we study harmonic analysis on the affine Poincaré group P aff , which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness properties of pseudo-differential operators on P aff. We also provide a necessary and sufficient condition on the operator-val...
Conference Paper
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The geometry measurement of involute gears is a key step within modelling, manufacturing, and performance evaluation to assure the delivery of high performance and cost-effective gears and gearboxes. Current challenges in manufacturing metrology can be summarized in five keywords: fast, accurate, reliable, flexible, and holistic. Moreover, modern n...