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The precise measurement of the spin speed of a high-speed autonomous unmanned aerial vehicle (HSA-UAV) is a key element in mastering flight stability, and the measurement of roll angle is the key to determining the accuracy of navigation control systems. We put forward a novel method for measuring roll angle. This method starts from the time–frequency domain analysis of the output signal of the geomagnetic sensor, extracts the time–frequency ridge of the time–frequency matrix (TFM) to obtain the spin speed of the HSA-UAV, and reconstructs the output signal of the geomagnetic sensor. It can calculate the roll angle when the calibration parameters of the geomagnetic sensor are unknown and have good engineering practical value. In addition, we also propose an improved nonlinear short-time Fourier transform with high-frequency resolution and a forward penalty dynamic path ridge-extraction method with frequency jump suppression to extract instantaneous frequency in the TFM. [ABSTRACT FROM AUTHOR]

Let { (N j , B j , L j) : 1 ⩽ j ⩽ m } be finitely many Hadamard triples in R . Given a sequence of positive integers { n k } k = 1 ∞ and ω = (ω k ) k = 1 ∞ ∈ { 1 , 2 , ... , m } N , let μ ω , { n k } be the infinite convolution given by μ ω , n k = δ N ω 1 − n 1 B ω 1 ∗ δ N ω 1 − n 1 N ω 2 − n 2 B ω 2 ∗ ⋯ ∗ δ N ω 1 − n 1 N ω 2 − n 2 ⋯ N ω k − n k B ω k ∗ ⋯. In order to study the spectrality of μ ω , { n k } , we first show the spectrality of general infinite convolutions generated by Hadamard triples under the equi-positivity condition. Then by using the integral periodic zero set of Fourier transform we show that if g c d (B j − B j) = 1 for 1 ⩽ j ⩽ m , then all infinite convolutions μ ω , { n k } are spectral measures. This implies that we may find a subset Λ ω , { n k } ⊆ R such that { e λ (x) = e 2 π i λ x : λ ∈ Λ ω , { n k } } forms an orthonormal basis for L 2 (μ ω , { n k }). [ABSTRACT FROM AUTHOR]

We present transition probabilities for 268 spectral lines of singly ionized chromium (Cr ii) in the wavelength region 208–414 nm. Branching fractions were measured in archival Fourier transform spectra of chromium-argon and chromium-neon hollow cathode lamps and a Penning discharge source. The branching fractions were combined with previously published experimental lifetimes of 14 levels, and with lifetimes from semiempirical calculations for 14 levels to give transition probabilities. The estimated uncertainties of the transition probabilities range from 10% to 26%. A comparison with previously published experimental transition probabilities shows discrepancies of up to a factor of 2.5 for lines around 213 nm. [ABSTRACT FROM AUTHOR]

Partially coherent Bessel-mode vortex-beams with radial coherence are introduced. The generated beams are fully coherent at pair of points along the same radial coordinate. The field is completely incoherent for pairs of points belonging to different angular positions. By using the coherent-mode structure of propagation invariant fields, the analytical expression of the propagated cross-spectral density, representing fields with radial coherence, is derived. It is shown that beams of this type can be generated in a Fourier transforming optical system. An important feature of the synthesized beams is their ability of being invariant under propagation. The behaviour of the degree of coherence is analysed in terms of the eigenvalues of the modal structure. A numerical ensemble of realizations, at both planes of the considered system, was generated. From this ensemble, the spectral intensity of the proposed beams was obtained. The numerical results show a well-defined principal thin ring of maximum intensity followed by secondary concentric rings, in complete agreement with theoretical predictions. We believe that presented scheme can trigger new research routes in the synthesis of fields with structured coherence. [ABSTRACT FROM AUTHOR]

Objective. Magnetic particle imaging (MPI) is a novel radiation-free medical imaging modality that can directly image superparamagnetic iron oxide tracers (SPIOs) with high sensitivity, temporal resolution, and good spatial resolution. The MPI reconstruction task can be formulated mathematically as a Fredholm integral problem, but the concrete inversion is not easily possible because of the particle dynamics or scanner issues. Measurement based system matrix inversion takes these factors into account, but prior measurement and calibration are time consuming. Approach. We proposed a direct imaging method based on the weighted sum of harmonic signals. The harmonic signals with spatial information are obtained by the short-time Fourier transform, and odd harmonic components are selected for recombination and then mapped to the sampling trajectory to image the concentration distribution of SPIOs. In addition, we adopt a normalized-weighted sum of harmonics to improve the resolution of the native image. Main results. The effectiveness of the proposed method is verified by simulation imaging experiments and our in-house scanner-based experiments. Quantitative evaluation results show that compared with traditional methods, the structural similarity improved by 48%, mean square error decreased by 88%, and signal-to-artifact ratio increased by 2.5 times. Significance. The proposed method can rapidly image the concentration distribution of nanoparticles without any prior calibration measurements and reduce the blur of MPI images without deconvolution, which has the potential to be implemented as a multi-patch imaging method in MPI. [ABSTRACT FROM AUTHOR]

The study of solar activity holds special importance since the changes in our star's behavior affect both the Earth's atmosphere and the conditions of the interplanetary environment. They can interfere with air navigation, space flight, satellites, radar, high-frequency communications, and overhead power lines, and can even negatively influence human health. We present here a machine learning-based prediction of the evolution of the current sunspot cycle (solar cycle 25). First, we analyze the Fourier Transform of the total time series (from 1749 to 2022) to find periodicities with which to lag this series and then add attributes (predictors) to the forecasting models to obtain the most accurate result possible. Consequently, we build a trained model of the series considering different starting points (from 1749 to 1940, with 1 yr steps), applying Random Forests, Support Vector Machines, Gaussian Processes, and Linear Regression. We find that the model with the lowest error in the test phase (cycle 24) arises with Random Forest and with 1915 as the start year of the time series (yielding a Root Mean Squared Error of 9.59 sunspots). Finally, for cycle 25 this model predicts that the maximum number of sunspots (90) will occur in 2025 March. [ABSTRACT FROM AUTHOR]

The purpose of this study was to present a new setup for time-resolved measurements of the interactions between gas jets and flexible surfaces. Such interactions are dominated by characteristic surface deformations and gas-driven surface waves. Previous works have studied the gasâ€"surface interaction only in a sectional plane but not as a three-dimensional problem. In our setup, surface deformations and waves were generated by the impingement of a supersonic jet on a flexible surface made of a silicon membrane. The inlet pressure of the Laval nozzle was varied from 0.8 bar to 3 bar and the nozzle surface distance was set in the range of 30â€"120 mm with respect to the flat surface. The entire surface area and its behavior were recorded using a high-speed camera. The evaluation was based on the pixel intensity values of the recorded surface images during the jet impingement. A fast Fourier transformation was applied to the results to determine the dominant frequencies of surface movements in detail. From this, low- and high-frequency events on the surface can be derived. Correlations between the main process parameters, nozzle distance, nozzle inlet pressure and characteristic surface behavior were deduced and mapped. [ABSTRACT FROM AUTHOR]

A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing optimal non Cartesian Fourier sampling patterns is a difficult nonconvex problem by bringing to light two optimization issues. The first one is the existence of a combinatorial number of spurious minimizers for a generic class of signals. The second one is a vanishing gradient effect for the high frequencies. We conclude the paper by showing how using large datasets can mitigate the first effect and illustrate experimentally the benefits of using stochastic gradient algorithms with a variable metric. [ABSTRACT FROM AUTHOR]

We have numerically and experimentally observed the soliton pulsation with obvious breathing behavior in the anomalous fiber laser mode-locked by a nonlinear polarization rotation technique. The numerical study of the soliton pulsation with breathing behavior was analyzed through the split-step Fourier method at first, and it was found that the phase difference caused by the polarization controller would affect the breathing characteristics. Then, taking advantage of the dispersive Fourier transform technique, we confirmed the breathing characteristic of soliton pulsation in the same fiber laser as the simulation model experimentally. These results complement the research on the breathing characteristic of soliton pulsation. [ABSTRACT FROM AUTHOR]

The Fourier transformation is an effective and efficient operation of Gaussianization at the one-point level. Using a set of N -body simulation data, we verified that the one-point distribution functions of the dark matter momentum divergence and density fields closely follow complex Gaussian distributions. The one-point distribution function of the quotient of two complex Gaussian variables is introduced and studied. Statistical theories are then applied to model one-point statistics about the growth of individual Fourier modes of the dark matter density field, which can be obtained by the ratio of two Fourier-transformed cosmic fields. Our simulation results proved that the models based on the Gaussian approximation are impressively accurate, and our analysis revealed many interesting aspects of the growth of dark matter’s density fluctuation in Fourier space. [ABSTRACT FROM AUTHOR]

Magnetic resonance imaging (MRI) is a medical imaging technique which is widely used in clinical routine. Standard imaging methods lead to so-called contrast-weighted images. The contrast arises from several tissue-related parameters such as the relaxation times T 1 and T 2. The aim in quantitative MRI (qMRI) is an estimation of these quantitative parameters. Magnetic resonance fingerprinting (MRF) is a promising technique in qMRI that allows for the simultaneous determination of multiple tissue-related parameters within a short acquisition time. The conventional MRF method utilizes an approximate inverse Fourier transformation for the highly undersampled data in the Fourier domain, leading to aliasing errors in the reconstructed magnetization courses. Computationally expensive statistical MRF modeling approaches overcome this issue by modeling the data directly in the Fourier domain. However, this leads to a non-convex and large-scale optimization task that is challenging to solve and requires expensive calculations. We compare two recent approaches, namely the conventional MRF method and a statistical MRF modeling approach based on Bayesian statistics in terms of their accuracy, reliability and computational costs. The comparison is carried out for simulated data with known ground truth for different signal-to-noise ratios, in the presence of errors in the physical model, and for several Fourier domain sampling schemes. It is demonstrated that a residual analysis can help to decide if the conventional MRF method is sufficient or if the complex Bayesian Fourier domain modeling approach can lead to a significant improvement. [ABSTRACT FROM AUTHOR]

This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local form. To achieve it, we use the theory of generalized functions and the Fourier transform in the space of tempered distributions S ′ . We show that the non-local operator domain is not defined on the whole functional space but on a subset of it. Moreover, we prove that these functions and their derivatives are bounded in all R 3 and, consequently, the Riemann tensor is regular and the scalar curvature invariants do not present any spacetime singularity. Finally, we explore what conditions we need to satisfy so that the solutions of the linearized equations of motion exist in S ′ . [ABSTRACT FROM AUTHOR]

In this study, we investigate Airy, cos-Airy, and cosh-Airy beam lasers with optical vortex (OV). Then, taking into account the Fourier transform, we examine and compare the propagation of these beams in a strong nonlinear system. The results indicate that by changing the input power p 0 and the parameters b and propagation length, the location of OV displaces. It is shown that nonlinearity is one of the parameters that control OV in optical systems used in these types of lasers. An important property in these beams is their direction variation due to the change in the mentioned parameters, which can be used in applications such as beam switching. [ABSTRACT FROM AUTHOR]

For acoustic procedures which rely on the speed of sound to derive process parameters, the determination of the acoustic time of flight (TOF) is essential. In this work, a method for the determination of the TOF is presented. It is intended for reverberant and noisy environments and can be applied in the gas holdup determination in bubbly liquids via acoustic transmission tomography for example. The method includes the selection and design of the transmitted signal to optimize the disambiguate of the autocorrelation, the narrowing of the time window based on the fractional Fourier transform to accelerate the TOF estimation. Furthermore, it includes the consideration of the system-induced signal distortion through prior quasi-anechoic measurements and the sparse reconstruction of the spatial impulse response for TOF estimation using non-negative sparse deconvolution algorithms. The method is tested analytically on numerically generated signals and various sparse deconvolution algorithms are investigated with respect to their applicability and limitations. [ABSTRACT FROM AUTHOR]

Multi-path (or multi-mode) entanglement has been proved to be a useful resource for sub-shot-noise sensitivity of phase estimation, which has aroused much research interest inquantum metrology recently. Various schemes of multi-path interferometers based on optical systems have been put forward. Here, we study a multi-state interferometer with multi-level atoms by projective measurements. Specifically, we investigate its ultimate sensitivity described by quantum Fisher information theory and find that the Cramerâ€"Rao bound can be achieved. In particular, we investigate a specific scheme to improve the sensitivityof magnetometery with a three-state interferometry delivered by a single nitrogen-vacancy (NV) center of diamond with tailor pulses. The impacts of imperfections of the atomic beam-splitter, described by the three-level quantum Fourier transform, on the sensitivity of phase estimation is also discussed. [ABSTRACT FROM AUTHOR]

We rigorously investigate the rapidly oscillating contributions in the sinc-function representation of the Dirac delta function and the Fourier transform of the Coulomb potential. Beginning with a derivation of the standard integral representation of the Heaviside step function, we examine the representation of the Dirac delta function that contains a rapidly oscillating sinc function. By contour integration, we prove that the representation satisfies the properties of the Dirac delta function, although it is a function divergent at nonzero points. This is a good pedagogical example demonstrating the difference between a function and a distribution. In most textbooks, the rapidly oscillating contribution in the Fourier transform of the Coulomb potential into the momentum space has been ignored by regulating the oscillatory divergence with the screened potential of Wentzel. By performing the inverse Fourier transform of the contribution rigorously, we demonstrate that the contribution is a well-defined distribution that is indeed zero, even if it is an ill-defined function. Proofs are extended to exhibit that the Riemannâ€"Lebesgue lemma can hold for a sinc function, which is not absolutely integrable. [ABSTRACT FROM AUTHOR]

The extraction of weak fault signatures with periodic impulse characteristics is a crucial aspect of detecting an early fault of bearing. In order to suppress the interference of background noise to the weak fault signatures extraction by variational mode decomposition (VMD), some scholars recently proposed to use fractional Fourier transform (FRFT) to make the weak fault signatures concentrate more energy in the narrowband, which is called VMD-FRFT. Nevertheless, VMD-FRFT is more sensitive to the initial center frequency (ICF) than VMD according to our study, which will make it derive undesirable mode components due to unreasonable ICFs. Inspired by the resonant demodulation method to find the appropriate frequency band for demodulation, an improved VMD-FRFT with the guidance of ICF is proposed, which is to take the center frequencies corresponding to K selected frequency bands as the initial values of VMD-FRFT. Hence, the modal components hidden in multiple resonant frequency bands can be obtained in terms of performing iterative optimization. In this paper, a novel indicator named reciprocal of spectral autocorrelation smoothness index being sensitive to the periodic impulses is introduced to detect resonance frequency bands. Both simulated and experimental examples are used to verify the proposed method. The results show that the proposed method can effectively identify weak faults and detect bearing faults at an earlier time than other methods such as Infogram, reciprocal of spectral smoothness index and improved VMD. [ABSTRACT FROM AUTHOR]

Objective. Fetal ECG (FECG) plays an important role in fetal monitoring. However, the abdominal ECG (AECG) recorded at the maternal abdomen is affected by various noises, making the extraction of FECG a challenging task. The main objective is to present a novel approach to FECG extraction using short time Fourier transform (STFT) and generative adversarial networks (GAN). Methods. Firstly, the AECG signals are transformed from one-dimensional (1D) time domain to two-dimensional (2D) time-frequency domain by using the STFT. Secondly, the 2D-STFT coefficients of FECG are estimated by the GAN model in the time-frequency domain. Finally, after the inverse STFT, the FECG can be reconstructed in the time domain. Main results. Experimental results on two databases demonstrate the effectiveness of the proposed method. Specifically, the SE, PPV and F 1 of the proposed method on PCDB are 92.37 ± 3.78%, 93.69 ± 3.96% and 93.02 ± 3.81%, respectively. And the SE, PPV and F 1 on ADFECGDB are 90.32 ± 10.70%, 89.79 ± 9.26% and 90.05 ± 9.81%, respectively. Significance. Unlike the previous studies based on the elimination of maternal ECG in the 1D time domain, the novelty of the proposed method relies on extracting the FECG directly from the AECG in the 2D time-frequency domain. It sheds some light to the topic of FECG extraction. [ABSTRACT FROM AUTHOR]

Fringe projection profilometry (FPP) is a three-dimensional (3D) shape measurement method that involves projecting fringe patterns onto the object. A phase map retrieved from these fringe images is used for reconstructing the 3D surface of the object. Fourier transform and phase-shifting are two of the widely used fringe analysis techniques for performing 3D shape measurement using FPP. Fourier transform profilometry (FTP) has the advantage of performing high-speed measurement due to its single-shot nature. However, the reconstructed 3D surface has artifacts and high noise, specifically on the edges. On the other hand, phase-shifting profilometry (PSP) has the advantage of higher accuracy (relatively less noise level) but compromises on measurement speed. In this research, we propose a deep learning method to enhance the quality of the FTP phase maps using an efficient deep learning model called phase map enhancement net (PMENet). PMENet takes an FTP phase map as input and predicts a high-quality phase map in a supervised manner by using the phase maps obtained from 18-step PSP as ground truth. The training dataset was generated using a virtual FPP system. Validations were conducted on both the simulated data (generated by virtual FPP system) and the real-world data. The experimental results demonstrate that the trained neural network model can successfully improve the quality of the 3D geometric reconstruction with FTP and reduced the mean and root-mean-square error by 66% and 43%, respectively. [ABSTRACT FROM AUTHOR]

The possibility to compute nucleon electromagnetic form factors in the time-like region by analytic continuation of their space-like expressions, obtained in the framework of a generic model of nucleons, has been explored. We have developed a procedure to analytically solve Fourier transforms of the nucleon electromagnetic current and hence to obtain form factors defined in all kinematic regions and fulfilling the first-principles requirements of analyticity and unitarity. The results obtained in the particular case of the Skyrme model are discussed and compared to data, both in the space-like and time-like region. [ABSTRACT FROM AUTHOR]

The Wigner functions for the coherent states of a particle on a circle are discussed. The nontrivial analytic forms of these functions are derived. The classicality of the circular coherent states existing in the literature as well as the new ones constructed by means of the Fourier transformation of the Gaussian is compared based on negativity of the Wigner function. [ABSTRACT FROM AUTHOR]

According to the properties of Fourier transform, Fourier single-pixel imaging uses the illumination lights with cosine distributions to obtain the Fourier spectrum of the object, and then apply the inverse Fourier transform to reconstruct the spatial information of the object. This technique does not require detector arrays, such as charge coupled device and has proven to be insensitive to distortion, which is a great improvement over traditional photography techniques. In this manuscript, we present a detailed analysis and discussion on the signal-to-noise ratio (SNR) of Fourier single-pixel imaging. Compared with conventional imaging whose SNR is independent of pixel number N, Fourier single-pixel imaging achieves an improved SNR which is up to N times as high as the dynamic range of detection. Furthermore, this SNR benefit is further confirmed experimentally, in cases of one dimension and two dimensions. [ABSTRACT FROM AUTHOR]

Objective. Disease may cause changes in an individual's respiratory pattern, which can be measured as parameters for disease evaluation, usually through manually annotated polysomnographic recordings. In this study, a machine learning model based on nasal airflow and respiratory effort of the chest and abdomen is proposed to automatically identify respiratory events, including normal breathing, hypopnea and apnea. Approach. The nasal airflow and chest–abdominal respiratory effort signals were collected by polysomnography (PSG). Time/frequency domain features, fractional Fourier transform features and sample entropy were calculated to obtain feature sets. Features selected through statistical analysis were used as input variables of the machine learning model. The performance of different input combinations on different models was studied and cross-validated. Main results. The dataset included PSG sleep records of 60 patients provided by the Chinese People's Liberation Army General Hospital. The extreme gradient boosting-based model (XGBoost) performed best in several models with an accuracy of 0.807 and a F1 score of 0.807, depending on the combination of nasal airflow and two respiratory effort signals. The precision for normal breathing, hypopnea and apnea events were 0.764, 0.789 and 0.871, respectively. In addition, the recall scores were 0.833, 0.768 and 0.823 for normal breathing, hypopnea and apnea events, respectively. Moreover, it was found that the standard deviation and kurtosis of nasal airflow were the most important features of the respiratory event detection model. Significance. Since nasal airflow and respiratory effort of the chest and abdomen contain the characteristics of respiratory events, their combined use can improve the classification performance for identification of respiratory events. With this method, respiratory events can be automatically detected and labeled from the PSG records, which can be used to screen for patients with sleep apnea–hypopnea syndrome. [ABSTRACT FROM AUTHOR]

Cosmic ray (CR) diurnal anisotropy and Forbush decreases (FDs), as well as the relationship between them, have received considerable study. Several astrophysicists have focused on the speculated impact of FDs on the amplitude of the diurnal CR variations on different timescales. In an attempt to disentangle the contribution of FDs, days of Forbush events are traditionally excluded while calculating the diurnal amplitude in individual neutron monitor (NM) data. But the implications of CR diurnal anisotropy on the magnitude of FDs are rarely investigated in detail. Recently, an effort was made, using a combination of Fast Fourier transform and FD-location algorithms, to account for the contribution of CR diurnal anisotropy on the number, magnitude, and timing of FDs. With some technical advancements, the efficiency of the software is tested in the current work using CR data measured by the oldest CR observatory (Climax) from 1953 to 2006. We find strong and statistically significant correlations between FD magnitude calculated from raw and Fourier transformed CR data and the amplitude of diurnal anisotropy. The relationship is stronger in the case of the Fourier transformed signal, lending credence to the idea that CR anisotropy is a part of Forbush events. In order to validate the observed relationship between the amplitude of CR diurnal variations, magnitude, and timing of FDs, large volumes of data from the Moscow, McMurdo, and Potchefstroom NMs were also analyzed. The significant CR intensity decreases (FD magnitude >5%) at the four stations were ranked according to their magnitudes. [ABSTRACT FROM AUTHOR]

In magnetic flux leakage testing, the lift-off effect shows that testing signal voltages vary with lift-off values. This has many adverse effects on detection and evaluation. This paper proposes a novel method for linearization of the lift-off effect in the spatial domain. The spatial analytical expression is obtained through magnetic dipole theory and the Fourier transform method. An analytical method to linearizethe lift-off effect is proposed. Further, the finite-element method and discrete Fourier transform method are applied to linearize the lift-off effect. Experimental studies are also conducted to verify the analytical results. The linear fitting function of the lift-off effect takes the form of Y = AX + B. When the spatial frequency ω is 35 mm−1, the linear fitting results of the simulation and experiment are Y = −0.23596X−2.0268 and Y = −0.23511X + 4.8152. The goodness of fit R2 is 0.9997 and 0.9975. The results show that the lift-off effect can be linearized in the spatial domain. The coefficient A is slightly affected by the defect size. The coefficient B is strongly related to the defect size. We consider these results to be quite significant. [ABSTRACT FROM AUTHOR]

An expansion of row Markov matrices in terms of matrices related to permutations with repetitions, is introduced. It generalises the Birkhoff–von Neumann expansion of doubly stochastic matrices in terms of permutation matrices (without repetitions). An interpretation of the formalism in terms of sequences of integers that open random safes described by the Markov matrices, is presented. Various quantities that describe probabilities and correlations in this context, are discussed. The Gini index is used to quantify the sparsity (certainty) of various probability vectors. The formalism is used in the context of multipartite quantum systems with finite dimensional Hilbert space, which can be viewed as quantum permutations with repetitions or as quantum safes. The scalar product of row Markov matrices, the various Gini indices, etc, are novel probabilistic quantities that describe the statistics of multipartite quantum systems. Local and global Fourier transforms are used to define locally dual and also globally dual statistical quantities. The latter depend on off-diagonal elements that entangle (in general) the various components of the system. Examples which demonstrate these ideas are also presented. [ABSTRACT FROM AUTHOR]

Based on the self-consistent phonon theory, the spectral energy density is calculated by the canonical transformation and the Fourier transformation. Through fitting the spectral energy density by the Lorentzian profile, the phonon frequency as well as the phonon relaxation time is obtained in one-dimensional nonlinear lattices, which is validated in the Fermi–Pasta–Ulam-β (FPU-β) and ϕ4 lattices at different temperatures. The phonon mean free path is then evaluated in terms of the phonon relaxation time and phonon group velocity. The results show that, in the FPU-β lattice, the phonon mean free path as well as the phonon relaxation time displays divergent power-law behavior. The divergent exponent coincides well with that derived from the Peierls–Boltzmann theory at weak anharmonic nonlinearity. The value of the divergent exponent expects a power-law divergent heat conductivity with system size, which violates Fourier's law. For the ϕ4 lattice, both the phonon relaxation time and mean free path are finite, which ensures normal heat conduction. [ABSTRACT FROM AUTHOR]

In this paper, we describe easy and cheap optics experiences for teaching undergraduate students the fundamental properties of Fourier transforms on an experimental basis. By exploiting the eye as the Fourier transforming device, a common magnifying lens, and quasi-coherent light from a small white LED, quantitative results can be easily obtained about the fundamental theorems used in Fourier analysis. The concept of coherence is also introduced in an elementary way. This approach has been successfully adopted to teach third-year students in physics, who operated in a completely autonomous way during the COVID-19 lockdown, without access to a laboratory. This proves the effectiveness of the method. Thanks to its experimental simplicity, it can easily be extended to teach and show the fundamental effects to a larger audience, including high-school students. [ABSTRACT FROM AUTHOR]

To prepare a hierarchical micro-nano structure FeF3·0.33H2O simply and economically, a one-pot method with dual surfactants was used. Scanning electron microscopy and a Fourier transformation infrared spectrometer revealed that polyvinyl pyrrolidone (PVP) regulates the morphology of the material, while cetyltrimethylammonium bromide (CTAB) can reshape FF@PVP, it can not only remove PVP at room temperature, but also obtain a hierarchical micro-nano structure. The electrochemical results show that the hierarchical micro-nano structure FF(1.5CTAB 0.5PVP) has the best electrochemical performance. It maintained a high specific capacity of 109.4 mAh g−1 after 100 cycles at 1 C. In particular, under the ultra-high rate discharge of 20 C, the ultra-high specific discharge capacity of 66.4 mAh g−1 was reached. The FF(1.5CTAB 0.5PVP)'s excellent electrochemical performance is mainly due to a large contact area between the electrolyte and active materials. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random field. The direct problem is shown to be well-posed by examining the well-posedness and regularity of the solution for the equivalent stochastic two-point boundary value problem in the frequency domain. For the inverse problem, the Fourier modulus of the diffusion coefficient of the random source is proved to be uniquely determined by the variance of the Fourier transform of the boundary data. As a phase retrieval for the inverse problem, the phaselift method with random masks is applied to recover the diffusion coefficient from its Fourier modulus. Numerical experiments are reported to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A combination of the Fourier transform and the maximum entropy method for estimating the frequency-wavenumber resolved power spectrum density is proposed. After illustrating the physical insight of the maximum entropy method by using synthetic test data, capability of the proposed method is tested using numerical simulation data. The method is also applied to experimental data obtained by the beam emission spectroscopy in the Large Helical Device. All of those examinations show that the proposed method provides more plausible results than conventional methods when the available spatial points are limited. [ABSTRACT FROM AUTHOR]

An effective registration framework between preoperative 3D computed tomography and intraoperative 2D x-ray images is crucial in image-guided therapy. In this paper, a novel 2D/3D hierarchical registration framework via principal-directional Fourier transform operator (HRF-PDFTO) is proposed. First, a PDFTO was established to obtain the in-plane translation and rotation invariance. Then, an initial free template-matching approach based on PDFTO was utilized to avoid initial value assignment and expand the capture range of registration. Finally, the hierarchical registration framework, HRF-PDFTO, was proposed to reduce the dimensions of the registration search space from n6 to n2. The experimental results demonstrated that the proposed HRF-PDFTO has good performance with an accuracy of 0.72 mm, and a single registration time of 16 s, which improves the registration efficiency by ten times. Consequently, the HRF-PDFTO can meet the accuracy and efficiency requirements of 2D/3D registration in related clinical applications. [ABSTRACT FROM AUTHOR]

A beam steering effect of high-power quantum cascade (QC) lasers emitting at ∼ 4.6 μm was investigated. The continuous wave (CW) output power of an uncoated, 6-mm-long, 7.5-μm-wide buried-heterostructure QC laser at 25 °C was as high as 854.2 mW. The maximum beam steering angle was offset by ± 14.2° from the facet normal (0°) in pulsed mode. The phenomenon was judged explicitly by combining the diffraction limit theory and Fourier transform of the spectra. It was also verified by finite element method software simulation and the calculation of two-dimensional (2D) effective-index model. The observed steering is consistent with a theory for coherence between the two lowest order lateral modes. Therefore, we have established an intrinsic linkage between the spectral instabilities and the beam steering by using the Fourier transform of the spectra, and further presented an extremely valid method to judge the beam steering. The content of this method includes both three equidistant peak positions in the Fourier transform of the spectra and the beam quality located between once the diffraction limit (DL) and twice the DL. [ABSTRACT FROM AUTHOR]

The problem of a solid sphere with uniform volume charge density is encountered in virtually all undergraduate calculus-based physics textbooks dealing with the topic of electromagnetism. This example illustrates well the use of Gauss's law and from there one can easily derive all the quantities of interest such as electrostatic field, potential, self-energy, and so on. Undergraduate physics majors are also well aware of the theory of Fourier transforms from having taken mathematics courses. Nevertheless, despite its great utility, the Fourier transform method is rarely mentioned as a powerful tool to solve physics problems at this level. To address this shortcoming, in this work we propose a possible scenario which may allow an instructor to introduce this powerful method to a proper undergraduate audience without any major pedagogical drawback. The case study that we choose is that of a solid sphere with uniform volume charge density. Specifically, we show the calculation of its electrostatic self-energy by using Fourier transform techniques. The main idea of this work is to draw reader's attention to the versatility of the approach that can, in principle, be applied to other more geometrically complicated bodies where Gauss's law does not lead to simple solutions. Concurrently, this work also provides instructional approaches that intertwine content-specific and pedagogical viewpoints that can be useful to all undergraduate students and teachers who wish to enhance their command of the subject. [ABSTRACT FROM AUTHOR]

In physical optics, Fresnel diffraction matters. The single Fourier transform method has been widely used in Fresnel diffraction calculation and can perform the direct computation of the output field with high efficiency. Based on a phase-space analysis, we find that the conventional single Fourier transform method cannot correctly deal with the full bandwidth of the input field. Aliasing occurs with high-frequency components because the bandwidth transfer capacity of the conventional method is insufficient, which greatly deteriorates the calculation accuracy. To address this serious problem, we propose a single Fourier transform-based full-bandwidth Fresnel diffraction calculation method. By rearrangement of the sampling resources, all the frequency components can be correctly transferred for accurate, efficient, and flexible Fresnel diffraction calculation. [ABSTRACT FROM AUTHOR]

In this paper, multiple interference components in a fiber Mach–Zehnder interferometer sensor and their influence on wavelength shift tracing were studied, based on which a frequency filtering method followed by inverse Fourier transform was proposed to improve the sensor's response accuracy. Firstly, multiple interference components in the transmission spectrum of a fiber MMF-SMF-MMF structure were simulated, and environmental response discrepancy in different components was calculated. Then, Fourier transform was performed on the transmission spectrum followed by frequency filtering to pick out the dominant interference component. An inverse Fourier transform was then carried out to obtain the wavelength shift which was undisturbed by minor interference components. The method was demonstrated by temperature and ambient refractive index (RI) calibration experiments as well as verification tests. The deviation between temperature sensitivity obtained with and without frequency filtering was 39%. The verification test at 80 °C was carried out and the measurement error was three times lower due to frequency filtering. For RI sensing, the deviation between sensitivity obtained with and without filtering was 19%. Measurement errors at 1.3706 of RI were seven times decreased after frequency filtering. Due to its simplicity and efficiency, the proposed method is believed to have extensive application prospects in sensing fields, especially when high-precision temperature and RI sensing are desired. [ABSTRACT FROM AUTHOR]

Quantum information processing protocols have great advantages over their classical counterparts, especially on cryptography. Secure multi-party computation is one of the most important issues and has been extensively studied in cryptography. It is of both theoretical and practical significance to develop the quantum information processing protocols for secure multi-party computation. In this paper, we consider the secure multi-party computation for n-variable polynomial functions over the finite field GF(d). We propose two protocols using quantum resources to compute the function within a one-time execution. One is based on d-level mutually unbiased (orthonormal) bases with cyclic property and the other takes advantage of quantum Fourier transform. Analytical results show that the proposed protocols are secure against a passive adversary with unlimited computing power, including colluding attack mounted by n − 2 parties. We also implement the second protocol of the special case d = 2 on the IBM Q Experience. In principle, our proposals can be experimentally realized in the arbitrary d dimension with the advances in realizations and controls of high-dimensional quantum computation. [ABSTRACT FROM AUTHOR]

Sample selection is a necessary preparation for weak lensing measurement. It is well-known that selection itself may introduce bias to the measured shear signal. Using image simulation and the Fourier_Quad shear measurement pipeline, we quantify the selection bias in various commonly used selection criteria (signal-to-noise ratio, magnitude, etc.). We propose a new selection criterion defined in the power spectrum of the galaxy image. This new selection criterion has a low selection bias, and it is particularly convenient for shear measurement pipelines based on Fourier transformation. [ABSTRACT FROM AUTHOR]

Plasma-activated water (PAW) represents a promising green antibacterial agent for biomedical and agricultural applications. In this study, a novel AC multi-needle-to-water discharge device was developed to investigate the effects of gas flow on the generation and chemical composition of PAW. It is shown that the concentrations of and N(III) (and) in the PAW both increased with an extension of the plasma-processing time and a reduction of the gas-flow rate. The absorption of gas-phase products carried by the gas flow from the discharge chamber was found to be beneficial for the generation of both and N(III) in the PAW at a gas flow rate of 20–60 L h−1, yet their concentrations were still lower than those without any feeding gas. As opposed to or N(III), the concentration in the plasma-activated phosphate buffer solution (PAPBS) increased under stronger gas flows and was almost unaffected by absorption in PAPBS. The pH value of PAW increased at higher gas flow rates. A comparison of the N(III) in PAW and PAPBS reflects the effects of the reactions of and in the two different working liquids. To quantify the effects of gas flow on the discharge characteristics, gas temperatures were calculated from the optical emission spectra and were proven to be flow-independent near the discharge channel. Fourier transform infrared (FTIR) measurements of the gaseous products during the discharge, and further analysis of possible reaction pathways indicated that by controlling the gas flow in the multi-needle-to-water discharge system, the concentration of long-lived species in PAW could be tuned, which might favor the generation of These findings contribute to a better understanding of effective electric discharge-related mechanisms for enhancing the biochemical and chemical activities of PAW. [ABSTRACT FROM AUTHOR]

We developed a stent flow sensor using micro-electromechanical systems (MEMS) technology in order to measure airflow in the airways of laboratory animals. An airflow waveform contains a respiration signal produced by lung motion and heartbeats as these functions are physically connected. This enables both respiration and heart functions to be evaluated under unrestrained and unanesthetized conditions during drug development. Using MEMS technology, we fabricated a tube flow sensor based on a thermal principle, and the stent structure was produced by photolithography and wet etching. The fabricated flow sensor and stent were integrated via a connection area on both elements. In the proof-of-concept trial, we verified that the flow sensor was placed in the center of the tube by expanding the stent. We evaluated the flow detection characteristics, sensor output vs flow rate and sensor response and used the developed stent flow sensor to measure the airflow in the airway of a rat. The respiration and heartbeat signals were successfully identified from the airflow waveform by applying Fourier transform analysis. [ABSTRACT FROM AUTHOR]

The joint time–frequency (TF) distribution is a critical method of describing the instantaneous frequency that changes with time. To eliminate the errors caused by strong modulation and noise interference in the process of time-varying fault feature extraction, this paper proposes a novel approach called second-order time–frequency sparse representation (SOTFSR), which is based on convex optimization in the domain of second-order short-time Fourier transform (SOSTFT) where the TF feature manifests itself as a relative sparsity. According to the second-order local estimation of the phase function, SOSTFT can provide a sparse TF coefficient in the short-time Fourier transform (STFT) domain. To obtain the optimal TF coefficient matrix from noisy observations, it is innovatively formulated as a typical convex optimization problem. Subsequently, a multivariate generalized minimax concave penalty is employed to maintain the convexity of the least-squares cost function to be minimized. The aim of the proposed SOTFSR is to obtain the optimal STFT coefficient in the TF domain for extraction of time-varying features and for perfect signal reconstruction. To verify the superiority of the proposed method, we collect the multi-component simulation signals and the signals under variable speed from a rolling bearing with an inner ring fault. The experimental results show that the proposed method can effectively extract the time-varying fault characteristics. [ABSTRACT FROM AUTHOR]

This paper presents a single-shot phase extraction approach based on a deep convolutional generative adversarial network that generates a phase map and a quality mask from an input fringe pattern image. A novel loss function is proposed, and a large-scale (28 800 samples) real fringe pattern dataset is collected to train the network. The experiments demonstrate that the proposed method achieves significantly improved phase extraction accuracy and overcomes the main limitations of Fourier transform profilometry. In addition, the proposed method presents excellent performance for real-time computing, reaching approximately 100 f s−1 with a single GPU. Moreover, the proposed learning-based approach can automatically perform denoising and phase extraction, without any manually set parameters. [ABSTRACT FROM AUTHOR]

Rotating machinery is a primary element of mechanical equipment, and thus fault diagnosis of its key components is very important to improve the reliability and safety of modern industrial systems. The key point to diagnose the faults of these components is to extract effectively the hidden fault information. However, the actual vibration signals of rotating machinery have nonlinear and non-stationary characteristics, so traditional signal decomposition methods are unable to extract the frequency components accurately, leading to spectrum overlap of the decomposed sub-signals. Therefore, a rotating machinery fault diagnosis approach based on Fourier transform multi-filter decomposition (FTMFD), fuzzy entropy (FE), joint mutual information maximization (JMIM), and a light gradient boosting machine (LightGBM), is proposed in this paper. FTMFD is used to extract the frequency domain information of the raw vibration signals, whereas FE is used to calculate and extract the fault information of the decomposed sub-signals. Then feature selection is carried out by using JMIM to reduce the influence of redundant features on data analysis and classification accuracy. Furthermore, LightGBM is used to rank the candidate features and outputs the fault diagnosis result. Experimental results from two real datasets show that the proposed method achieves higher accuracy with fewer features than some existing methods for fault recognition. Various working conditions are also considered and verified. [ABSTRACT FROM AUTHOR]

We prove a Hölder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function v on from its Fourier transform given on [−r, r]d. This estimate relies on a Hölder stable continuation of from [−r, r]d to a larger domain. The related reconstruction procedures are based on truncated series of Chebyshev polynomials. We also give an explicit example showing optimality of our stability estimates. [ABSTRACT FROM AUTHOR]

Two mathematical phenomena with applications in physics are: superoscillations, in which band-limited functions oscillate more rapidly than their fastest Fourier component; and the transformation of almost any smooth function into a monochromatic oscillation under repeated differentiation. These are opposite phenomena, and one mutates into the other, i.e. superoscillations are destroyed, as the number of derivatives increases. This behaviour is explained, and illustrated with an example. [ABSTRACT FROM AUTHOR]

Mode-locking lasers have not only produced huge economic benefits in industrial fields and scientific research, but also provided an excellent platform to study diverse soliton phenomena. However, the real-time characterization of the ultrafast soliton dynamics remains challenging for traditional electronic instruments due to their relatively low response bandwidth and slow scan rate. Consequently, it is urgent for researchers to directly observe these ultrafast evolution processes, rather than just indirectly understand them from numerical simulations or averaged measurement data. Fortunately, dispersive Fourier transformation (DFT) provides a powerful real-time measurement technique to overcome the speed limitations of traditional electronic measurement devices by mapping the frequency spectrum onto the temporal waveform. In this review, the operation principle of DFT is discussed and the recent progress in characterizing the ultrafast transient soliton dynamics of mode-locking lasers is summarized, including soliton explosions, soliton molecules, noise-like pulses, rogue waves, and mode-locking buildup processes. [ABSTRACT FROM AUTHOR]

We consider a Dirichlet to Neumann operator arising in a model for water waves, with a nonlocal parameter a ∈ (−1, 1). We deduce the expression of the operator in terms of the Fourier transform, highlighting a local behaviour for small frequencies and a nonlocal behaviour for large frequencies. We further investigate the Γ-convergence of the energy associated to the equation , where W is a double-well potential. When a ∈ (−1, 0] the energy Γ-converges to the classical perimeter, while for a ∈ (0, 1) the Γ-limit is a new nonlocal operator, that in dimension n = 1 interpolates the classical and the nonlocal perimeter. [ABSTRACT FROM AUTHOR]

In this study, a novel gas sensor is proposed based on a three-dimensional reduced graphene oxide/polyaniline (3D RGO/PANI) hybrid, which is synthesized by a hydrothermal method for detecting NH3 gas at room temperature. The 3D RGO/PANI hybrid is characterized by field emission-scanning electron microscopy, Fourier transform infrared and x-ray diffraction. The specific surface area is analyzed using the Brunauer–Emmett–Teller (BET) equation. The as-synthesized sensing materials with an appropriate amount of polyaniline nanowires (PANI-NWs) can effectively prevent aggregation of the neighboring graphene sheets and directly act as adsorption sites for NH3 molecules. In comparison with its pure 3D RGO counterpart, the 3D RGO/PANI (1:1) hybrid exhibits 44.7 times enhanced response to 100 ppm NH3, suggesting the remarkable effect of PANI-NWs in improving the sensitivity. This work gives new insights into boosting the sensitivity and selectivity of detecting NH3 gas by incorporating PANI-NWs into 3D RGO. [ABSTRACT FROM AUTHOR]

This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundaries of perfectly conducting obstacles. We show that the smallest strip containing the unknown object can be approximately determined by the multi-frequency backscattering far field data at two opposite observation directions. The proof is based on the Kirchhoff approximation and Fourier transform. Such a strip is then reconstructed by an indicator, which is the absolute value of an integral of the product of the data and some properly chosen function over the frequency interval. With the increase of the number of the backscattering data, the location and shape of the underlying object can be reconstructed. Numerical examples are conducted to show the validity and robustness of the proposed sampling method, even with moderately sized frequencies. The numerical examples also show that the concave part of the underlying object can be well reconstructed, and the different connected components of the underlying object can be well separated. [ABSTRACT FROM AUTHOR]

The similarity between in-plane directions of spatial optics and overlapped time ranges of temporal optics is introduced as a new rule of the space–time duality. Applying this rule, an optical dual random phase encoding (DRPE) cryptosystem in the temporal anamorphic fractional Fourier transform (TAFrFT) domain is proposed for physical-level protection of time-varying signals. The structure of a TAFrFT system is an anamorphic time lens (ATL) sandwiched by two identical dispersion elements. The additional key provided by a TAFrFT system is only related to phase profile of the involved ATL, leading to a dispersion-independent manner of key updating as well as an enlarged key space (KS) in comparison with the conventional temporal FrFT and Fresnel transform system. This manner of key updating has potential as a one-time key strategy to evade the intrinsic linearity and symmetry weakness of DRPE-like temporal cryptosystems, due to the updating speed being comparable to the frame rate of plaintext signals. As the temporal counterpart of a spatial optical device composed of cylindrical lenses along different directions, an ATL is designed as an equal-spaced array of time lenses with unipolar phase, constant extension, and varying phase height. Implemented by an arbitrary waveform generator (AWG)-driven electro-optic phase modulator (EOPM), the time interval of adjacent time lenses, extension of each time lens, and the standard phase height are optimally designed as functions of the AWG bandwidth BM and the EOPM damage phase threshold. By numerical simulations, a 16-slot input optical Gaussian pulse sequence with half pulse width of 10 ps and frame length of 2000 ps is encrypted with a KS near provided by ATLs at parameters GHz and radians under the state of the art, enough for resistance to brute-force attacks. [ABSTRACT FROM AUTHOR]