In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R + , which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis....
Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space a...
The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively...
To improve the accuracy of infrared radiation characteristics measurement in the aviation field, an infrared Fourier transform imaging spectrometer based on a double-swing solid angle reflector was designed. This imaging spectrometer operates in the...
This work describes a post-processing scheme for multiphase flow systems to characterize primary atomization. The scheme relies on the 2D fast Fourier transform (FFT) to separate the inherently multi-scale features present in the flow results. Emphas...
In this paper, we propose an area-efficient short-time Fourier transform (STFT) processor that can perform time–frequency analysis of non-stationary signals in real time, which is essential for voice or radar-signal processing systems. STFT pro...
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numeri...
Broken rotor bars in induction motors make up one of the typical fault types that are challenging to detect. This type of damage can provoke adverse effects on the motors, such as mechanical and electrical stresses, together with an increase in elect...
Time–frequency analysis is an important tool used for the processing and interpretation of non-stationary signals, such as seismic data and remote sensing data. In this paper, based on the novel short-time fractional Fourier transform (STFRFT),...
This paper proposes a simple and efficient FPGA-based architecture of the overlapping/windowing and overlap-add methods for real-time FFT/IFFT-based signal processing algorithms. The analyzed signal is divided into short-time overlapping frames that...
It is of importance but great difficulty to objectively and quantitatively evaluate the sustainable development level, especially in the weight determination process and uncertainty evaluation. The traditional weight determination methods hardly refl...
In this paper, we propose a deep convolutional neural network for camera based wildfire detection. We train the neural network via transfer learning and use window based analysis strategy to increase the fire detection rate. To achieve computational...
Near-infrared spectroscopy is a non-invasive, rapid, and efficient analytical method widely employed in agricultural quality assessment. This study aims to explore the potential of Fourier transform near-infrared (FT-NIR) spectroscopy in the analysis...
In response to the high demand of the operation reliability and predictive maintenance, health monitoring and fault diagnosis and classification have been paramount for complex industrial systems (e.g., wind turbine energy systems). In this study, da...
Volumetric optoacoustic tomography has been shown to provide unprecedented capabilities for ultrafast imaging of cardiovascular dynamics in mice. Three-dimensional imaging rates in the order of 100 Hz have been achieved, which enabled the visualizati...
To address the problem of on-line dissolved gas analysis (DGA) of a power transformer, a Fourier transform infrared (FT-IR) spectrometer was used to develop an analysis instrument. Carbon monoxide (CO), carbon dioxide (CO2), methane (CH4), ethane (C2...
Many food products are subjected to quality control analyses for detection of surface residue/contaminants, and there is a trend of requiring more and more documentation and reporting by farmers regarding their use of pesticides. Recent outbreaks of...
Chitosan is a natural polysaccharide which has been authorized for oenological practices for the treatment of musts and wines. This authorization is limited to chitosan of fungal origin while that of crustacean origin is prohibited. To guarantee its...
With cotton fiber growth or maturation, cellulose content in cotton fibers markedly increases. Traditional chemical methods have been developed to determine cellulose content, but it is time-consuming and labor-intensive, mostly owing to the slow hyd...
This study performed non-destructive measurements of phenolic compounds in moringa powder using Fourier Transform Infrared (FT-IR) spectroscopy within a spectral range of 3500–700 cm−1. Three major phenolic compounds, namely, kaempferol,...
Change detection is a pivotal task in remote sensing information extraction, and leveraging the representation capabilities of large models has emerged as a promising direction in recent research. However, existing large-model-based change detection...
Fourier-transform imaging spectroscopy (FTIS) faces inherent limitations in spectral resolution due to the maximum optical path difference (OPD) achievable by its interferometer. To overcome this constraint, we propose a novel spectral super-resoluti...
Daily time series of microwave radiometer data obtained in one-orbit direction are full of observation gaps due to satellite configuration and errors from spatial sampling. Such time series carry information about the surface signal including surface...
Background: Blood pressure (BP) variability has been increasingly recognized as a predictor of cardiovascular and renal outcomes. However, the relevance of specific dynamic indices such as the maximum slope of systolic blood pressure (max SBP slope),...
For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically...
Direct analysis in real time (DART) is a recently developed ambient ionization technique for mass spectrometry to enable rapid and sensitive analyses with little or no sample preparation. After swab-based field sampling, the organothiophosphate malat...
As a result of increasing machines capabilities in modern manufacturing, machines run continuously for hours. Therefore, early fault detection is required to reduce the maintenance expenses and obviate high cost and unscheduled downtimes. Fault diagn...
Optical transmission gratings with quasi-sinusoidal surface-relief profiles were inscribed in IOG and Pyrex glasses and in Bi12GeO20, Er: LiNbO3, and Er: Fe: LiNbO3 crystals by microbeams of carbon, nitrogen, and oxygen ions at ion energies of 5, 6,...
With the growing number of cancer cases and deaths around the world, fast, non-invasive, and inexpensive screening is paramount. We examine the feasibility of such cancer detection using the X-ray scattering properties of nails in the canine model. A...
Purpose: To investigate the distribution and trend of corneal parameters in different age groups without corneal diseases. Methods: A retrospective cross-sectional study. We enrolled 2545 patients (5074 eyes) without corneal diseases (mean age 37.0 &...
Liquefied hydrogen storage vessels (LHSVs) are vulnerable to surface-crack initiation, propagation, and fracture on their surfaces because they are under high-pressure, low-temperature conditions. Defects can also occur in the coatings of the storage...
The calculation of symmetry in amputee gait is a valuable tool to assess the functional aspects of lower limb prostheses and how it impacts the overall gait mechanics. This paper analyzes the vertical trajectory of the body center of mass (CoM) of a...
This paper presents a detailed investigation into the application of transient Fourier analysis in select electrical engineering contexts. Two novel approaches for addressing transient analysis are introduced. The first approach combines the Fourier...
We apply the Discrete Fourier Transform to the construction of B-Spline curves to gain more insight into their structure. As a B-Spline curve is determined by its control polygon, this analysis is intimately linked to the Fourier analysis of the cont...
It is shown that the analysis of rotating circular images containing n = 2p−1 pixels, the state of which is described by variables of binary logic, and p is an integer, is expedient to carry out using digital spectra obtained using the Fourier&...
Recently Candida auris has emerged as a multi-resistant fungal pathogen, with a significant clinical impact, and is able to persist for a long time on human skin and hospital environments. It is a critical issue on the WHO fungal priority list and th...
This article presents a detailed study of the two-dimensional quaternion fractional Fourier transform (2D QFRFT) and investigates its role in the probabilistic analysis of quaternion-valued signals. The 2D formulation is constructed by applying fract...
Information on boll distribution within a cotton plant is critical to evaluate the adaptation and response of cotton plants to environmental and biotic stress in cotton production. Cotton researchers have applied available conventional fiber measurem...
In Bandpass Sampling Fourier Transform Spectroscopy, a comprehensive method for evaluating signal-to-noise ratio (SNR) has not yet been established. This paper employs an energy conservation approach to analyze the relationship of SNR between interfe...
Interferometric fiber-optic sensors provide very high measurement accuracy and come with many other benefits. As such, the study of signal processing techniques for fiber-optic interferometers in order to extract information about external perturbati...
This study aimed to forecast monthly PM2.5 concentrations in Zabol, one of the world’s most dust-prone regions, using four time series models: SARIMA, SARIMAX enhanced with Fourier terms (selected based on spectral peak analysis), TBATS, and a...
There is spiking interest in graph analysis, mainly sparked by social network analysis done for various purposes. With social network graphs often achieving very large size, there is a need for capable tools to perform such an analysis. In this artic...
Morphology is the most visible and distinct character of plant organs and is accepted as one of the most important tools for plant biologists, plant breeders and growers. A number of methods based on plant morphology are applied to discriminate in pa...
Non-Fourier heat behavior is an important issue for film material. The phenomenon is usually observed in some laser induced thermal responses. In this paper, the non-Fourier heat conduction problems with temperature and thermal flux relaxations are i...
This work investigates the possibility of applying Fourier Transform (FT) analysis of the force signal to follow fatigue behavior of metals under oscillatory displacement-controlled tests in uniaxial tension/tension. As a first step, three different...
Electroretinography (ERG) is a non-invasive method of assessing retinal function by recording the retina’s response to a brief flash of light. This study focused on optimizing the ERG waveform signal classification by utilizing Short-Time Fouri...
In this study, thermogravimetric analysis (TGA) was coupled with Fourier-transform infrared (FTIR) spectroscopy to systematically investigate the pyrolysis characteristics and mechanisms of cement fiberboard across varying heating rates. Experimental...
We generalize the classic Fourier transform operator F p by using the Henstock–Kurzweil integral theory. It is shown that the operator equals the H K -Fourier transform on a dense subspace of L p , 1 < p ≤ 2 ....
The concept of the phase space plays a key role in the analysis of oscillating signals. For a 1-D signal, the coordinates of the 2-D phase space are the observation time and the instant frequency. For measurements of propagating wave fields, the time...
Alzheimer’s disease is a challenge in modern healthcare due to its complex etiology and increasing prevalence. Despite advances, further understanding of Alzheimer’s disease pathophysiology is needed, particularly the role of Aβ neur...
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