Two-dimensional Fourier Transformation Research Articles

Numerical investigations of spatiotemporal dynamics of space-charge limited collisional sheaths

Electrostatic particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC) methods are used to compare the plasma dynamics of collisionless with collisional emissive sheaths in partially ionized environments. Space-charge limited emissive sheaths submersed in a plasma with a density of ∼1017 m−3 are examined using a PIC-DSMC solver, CHAOS. Collisionless emissive sheaths with plasma domains sufficiently long (30 and 60 Debye lengths, λD) are subject to strong oscillations due to two-stream electron instability, whereas emissive sheaths in weakly collisional conditions with a short domain (15 λD) exhibit self-spike (sawtooth) oscillations in the plasma field due to the trapped charge-exchange (CEX) ion population within the virtual cathode (VC) region. The two-stream electron instability leads to strong temporal fluctuations in the total emission current, with maximum deviations of 60% and 100% from the time-averaged current for the long plasma domains, whereas CEX collisions cause strong spikes in the emission current if the domain size is short. Our PIC-DSMC simulations show for the first time that the interaction of the two types of instabilities causes the strength of the self-spike to be weakened due to the strong fluctuations caused by the two-stream instability when a sufficiently long computational domain with ion-neutral collisions is employed. By conducting a two-dimensional Fast Fourier Transform (FFT) on the collisional and collisionless sheaths with long domains, we show that the transient evolution of CEX entrapment in the VC increases frequency of sheath oscillations up to two times the ion-acoustic frequencies observed in the collisionless sheath. CEX collisions weaken the VC region and result in a total emission current more than that obtained from the collisionless case for the same domain length. With a more rarefied neutral environment of 1019 m−3 in the plasma sheath, the total emission current increases only 4% in comparison with 14% for one order of magnitude denser environment, within 20 μs. In addition, the spike period is tested with different neutral temperatures and densities. While we do not observe any self-spike in the more rarefied environment, the spike period increased from 5 to 7.5 μs when the neutral temperature is increased from 300 to 2000 K in the denser environment with the simulation time of 20 μs.

Titchmarsh’s-type theorem for two-sided quaternion Fourier transform and sharp Hausdorff–Young inequality for quaternion linear canonical transform

In this work, we first introduce the two-sided quaternion Fourier transform and demonstrate its essential properties. We generalize Titchmarsh’s-type theorem in the framework of the two-sided quaternion Fourier transform. Based on the interaction between the quaternion Fourier transform and quaternion linear canonical transform we explore sharp Hausdorff–Young inequality for the quaternion linear canonical transform. The obtained result can be considered as a generalized version of sharp Hausdorff–Young inequality for the two-dimensional quaternion Fourier transformation in the literature.

Deep Learning Soft-Decision GNSS Multipath Detection and Mitigation.

A technique is proposed to detect the presence of the multipath effect in Global Navigation Satellite Signal (GNSS) signals using a convolutional neural network (CNN) as the building block. The network is trained and validated, for a wide range of C/N0 values, with a realistic dataset constituted by the synthetic noisy outputs of a 2D grid of correlators associated with different Doppler frequencies and code delays (time-domain dataset). Multipath-disturbed signals are generated in agreement with the various scenarios encompassed by the adopted multipath model. It was found that pre-processing the outputs of the correlators grid with the two-dimensional Discrete Fourier Transform (frequency-domain dataset) enables the CNN to improve the accuracy relative to the time-domain dataset. Depending on the kind of CNN outputs, two strategies can then be devised to solve the equation of navigation: either remove the disturbed signal from the equation (hard decision) or process the pseudoranges with a weighted least-squares algorithm, where the entries of the weighting matrix are computed using the analog outputs of the neural network (soft decision).

Decomposition of Submesoscale Ocean Wave and Current Derived from UAV-Based Observation

The consecutive submesoscale sea surface processes observed by an unmanned aerial vehicle (UAV) were used to decompose into spatial waves and current features. For the image decomposition, the Fast and Adaptive Multidimensional Empirical Mode Decomposition (FA-MEMD) method was employed to disintegrate multicomponent signals identified in sea surface optical images into modulated signals characterized by their amplitudes and frequencies. These signals, referred to as Bidimensional Intrinsic Mode Functions (BIMFs), represent the inherent two-dimensional oscillatory patterns within sea surface optical data. The BIMFs, separated into seven modes and a residual component, were subsequently reconstructed based on the physical frequencies. A two-dimensional Fast Fourier Transform (2D FFT) for each high-frequency mode was used for surface wave analysis to illustrate the wave characteristics. Wavenumbers (Kx, Ky) ranging between 0.01–0.1 radm−1 and wave directions predominantly in the northeastward direction were identified from the spectral peak ranges. The Optical Flow (OF) algorithm was applied to the remaining consecutive low-frequency modes as the current signal under 0.1 Hz for surface current analysis and to estimate a current field with a 1 m spatial resolution. The accuracy of currents in the overall region was validated with in situ drifter measurements, showing an R-squared (R2) value of 0.80 and an average root-mean-square error (RMSE) of 0.03 ms−1. This study proposes a novel framework for analyzing individual sea surface dynamical processes acquired from high-resolution UAV imagery using a multidimensional signal decomposition method specialized in nonlinear and nonstationary data analysis.

Molecular spectra and docking simulations investigated the binding mechanisms of tetracycline onto E. coli extracellular polymeric substances

Extracellular polymeric substances (EPS), which were an important fraction of natural organic matter (NOM), played an important role in various environmental processes. However, the heterogeneity, complexity, and dynamics of EPS make their interactions with antibiotics elusive. Using advanced multispectral technology, this study examined how EPS interacts with different concentrations of tetracycline (TC) in the soil system. Our results demonstrated that protein-like (C1), fulvic-like (C2), and humic-like (C3) fractions were identified from EPS. Two-dimensional synchronous correlation spectroscopy (2D–SF–COS) indicated that the protein-like fraction gave faster responses than the fulvic-like fraction during the TC binding process. The sequence of structural changes in EPS due to TC binding was revealed by two-dimensional Fourier Transformation Infrared correlation spectroscopy (2D–FTIR–COS) as follows: 1550 > 1660 > 1395 > 1240 > 1087 cm−1. It is noteworthy that the sensitivity of the amide group to TC has been preserved, with its intensity gradually increasing to become the primary binding site for TC. The integration of hetero-2DCOS maps with moving window 2D correlation spectroscopy (MW2DCOS) provided a unique insight into understanding the correlation between EPS fractions and functional groups during the TC binding process. Moreover, molecular docking (MD) discovered that the extracellular proteins would provide plenty of binding sites with TC through salt bridges, hydrogen bonds, and π-π base-stacking forces. With these results, systematic investigations of the dynamic changes in EPS components under different concentrations of antibiotic exposure demonstrated the advanced capabilities of multispectral technology in examining intricate interactions with EPS in the soil environment.

A new methodology of non-destructive testing in a set of two parallel immersed plates using time reversal process and leaky Lamb waves

Ultrasound has been identified as a suitable method for inspecting complex structures (such as nuclear reactors), as it can propagate through both liquids and steel elements to be inspected. Leaky Lamb waves have been extensively researched to detect damages in plate-shaped structures, which are waves that reemit bulk waves towards the surrounding fluid. An imaging method based on the time reversal of Lamb waves has been applied in preliminary work to detect the edge of a single immersed plate and a machined notch. In this study, the frequency-domain topological energy method is applied to a set of two parallel immersed plates to succeed in accurately localizing defects represented by the edges of the plates. Firstly, the behaviour of leaky Lamb waves is briefly addressed. A 2D-STFT (two-dimensional Short Time Fourier Transform) is then used to separate the different Lamb modes, which is a powerful tool for tracking the modes involved in the propagation over time. The Fast Topological Imaging Method (FTIM), which allows for faster computations with less data storage, is applied to the case of Lamb waves in a set of parallel plates. Lamb modes can be identified then selected to improve the analysis of the obtained images. An original methodology is proposed based on spots (maxima) analysis for interpreting the results of this topological energy and identifying the edges of the two plates. This process could be applied, in the same manner, to other scattering defects in ultrasound non-destructive testing of plates.

Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry by Matrix-Assisted Laser Desorption Ionization.

Two-dimensional Fourier transform ion cyclotron resonance (2D FTICR) mass spectrometry is a developing form of data-independent acquisition that allows for the simultaneous fragmentation and correlation of fragment ions to their precursors across a range of m/z values. The modern usage of 2D FTICR is performed using electrospray ionization (ESI) as the dried droplet preparation for matrix-assisted laser desorption ionization (MALDI) does not produce a consistent packet of ions over a number of scans. This work uses pneumatic spray techniques from mass spectrometry imaging to create a homogeneous surface for use with MALDI as an ionization source for 2D FTICR. A mixture of peptides and matrix was deposited onto a glass slide using an HTX pneumatic sprayer. MALDI was then used to ionize the peptide mixture for use with a standard 2D FTICR pulse sequence. The generated 2D spectrum reveals comparable structural information to spectra collected in a 1D experiment. Artifacts observed in the collected 2D MALDI spectra do not significantly differ from those expected from 2D ESI spectra.

General spatial photonic Ising machine based on the interaction matrix eigendecomposition method

The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly map an arbitrary problem to the Ising model. In this paper, we propose a general spatial photonic Ising machine based on the interaction matrix eigendecomposition method. The arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as ∼65% of the eigenvalues are required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this percentage decreases to below ∼20% for near-zero probability. The 4-spin experiments and error analysis demonstrate the Hamiltonian linear mapping and ergodic optimization. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of the multi-dimensional optical property.

Quantitative gait analysis and prediction using artificial intelligence for patients with gait disorders

Quantitative Gait Analysis (QGA) is considered as an objective measure of gait performance. In this study, we aim at designing an artificial intelligence that can efficiently predict the progression of gait quality using kinematic data obtained from QGA. For this purpose, a gait database collected from 734 patients with gait disorders is used. As the patient walks, kinematic data is collected during the gait session. This data is processed to generate the Gait Profile Score (GPS) for each gait cycle. Tracking potential GPS variations enables detecting changes in gait quality. In this regard, our work is driven by predicting such future variations. Two approaches were considered: signal-based and image-based. The signal-based one uses raw gait cycles, while the image-based one employs a two-dimensional Fast Fourier Transform (2D FFT) representation of gait cycles. Several architectures were developed, and the obtained Area Under the Curve (AUC) was above 0.72 for both approaches. To the best of our knowledge, our study is the first to apply neural networks for gait prediction tasks.

Geometric Properties of Water-ice Clouds as Observed from Jezero Crater in the First 600 sols with the NavCam Instrument On Board the Mars2020 Rover, Perseverance

In the first 600 sols of the Mars2020 mission, LS 5.6o – 316.8o, 46 cloud movies and 145 cloud surveys were collected to observe clouds at Jezero Crater, the landing site of the Perseverance Rover. Cloud movies were processed using the Mean-Frame Subtraction (MFS) method for revealing cloud structures, which were subsequently analyzed using digital-image processing. Two-dimensional Fast Fourier Transforms (2D-FFT) were used to compute cloud structure sizes ranging from 2.90 to 15.25 km for clouds between 30 and 50 km altitude, based on coincident Mars Climate Sounder vertical profiles of atmospheric water-ice. Same-value thresholding was used to detect the cloud structures in MFS-processed and projected cloud movies. The resolution dependence that was needed to resolve these structures over various thresholds was examined to find multifractal scaling of Mars clouds for resolutions between 0.1 and 1.6 km. We characterize the multiscaling observed in the images and its implications for the design of cloud-tracking cameras from the surface as well as for cloud-resolving models.

Evolution of Plumage Patterns in a Pattern Morphospace: A Phylogenetic Analysis of Melanerpine Woodpeckers.

AbstractPlumage patterns of melanerpine (Melanerpes-Sphyrapicus) woodpeckers are strikingly diverse. Understanding the evolution and function of this diversity is challenging because of the difficulty of quantifying plumage patterns. We use a three-dimensional space to characterize the evolution of melanerpine achromatic plumage patterns. The axes of the space are three pattern features (spatial frequency, orientation, and contrast) quantified using two-dimensional fast Fourier transformation of museum specimen images. Mapping plumage in pattern space reveals differences in how species and subclades occupy the space. To quantify these differences, we derive two new measures of pattern: pattern diversity (diversity across plumage patches within a species) and pattern uniqueness (divergence of patterns from those of other species). We estimate that the melanerpine ancestor had mottled plumage and find that pattern traits across patches and subclades evolve at different rates. We also find that smaller species are more likely to display horizontal face patterning. We promote pattern spaces as powerful tools for investigating animal pattern evolution.

Construction of synthetic anti-fouling consortia: fouling control effects and polysaccharide degradation mechanisms

The physical states and chemical components of bulk sludge determine the occurrence and development of membrane fouling in membrane bioreactors. Thus, regulation of sludge suspensions can provide new strategies for fouling control. In this study, we used “top-down” enrichment to construct a synthetic anti-fouling consortium (SAC) from bio-cake and evaluate its roles in preventing membrane fouling. The SAC was identified as Massilia-dominated and could almost wholly degrade the alginate solution (1,000 mg/L) within 72 h. Two-dimensional Fourier transformation infrared correlation spectroscopy (2D-FTIR-CoS) analysis demonstrated that the SAC induced the breakage of glycosidic bond in alginates. The co-cultivation of sludge with a low dosage of SAC (ranging from 0 to 1%) led to significant fouling mitigation, increased sludge floc size, and decreased unified membrane fouling index value (0.55 ± 0.06 and 0.11 ± 0.05). FTIR spectra and X-ray spectroscopy analyses demonstrated that the addition of SAC decreased the abundance of the O-acetylation of polysaccharides in extracellular polymeric substances. Secondary derivatives analysis of amide I spectra suggested a strong reduction in the α-helix/(β-sheet + random coil) ratio in the presence of SAC, which was expected to enhance cell aggregation. Additionally, the extracellular secretions of SAC could both inhibit biofilm formation and strongly disperse the existing biofilm strongly during the biofilm incubation tests. In summary, this study illustrates the feasibility and benefits of using SAC for fouling control and provides a new strategy for fouling control.

Use of 2D FFT and DTW in Protein Sequence Comparison.

Protein sequence comparison remains a challenging work for the researchers owing to the computational complexity due to the presence of 20 amino acids compared with only four nucleotides in Genome sequences. Further, protein sequences of different species are of different lengths; it throws additional changes to the researchers to develop methods, specially alignment-free methods, to compare protein sequences. In this work, an efficient technique to compare protein sequences is developed by a graphical representation. First, the classified grouping of 20 amino acids with a cardinality of 4 based on polar class is considered to narrow down the representational range from 20 to 4. Then a unit vector technique based on a two-quadrant Cartesian system is proposed to provide a new two-dimensional graphical representation of the protein sequence. Now, two approaches are proposed to cope with the varying lengths of protein sequences from various species: one uses Dynamic Time Warping (DTW), while the other one uses a two-dimensional Fast Fourier Transform (2D FFT). Next, the effectiveness of these two techniques is analyzed using two evaluation criteria-quantitative measures based on symmetric distance (SD) and computational speed. An analysis is performed on five data sets of 9 ND4, 9 ND5, 9 ND6, 12 Baculovirus, and 24 TF proteins under the two methods. It is found that the FFT-based method produces the same results as DTW but in less computational time. It is found that the result of the proposed method agrees with the known biological reference. Further, the present method produces better clustering than the existing ones.

Unsteady evolution of distributed roughness-induced vortices under re-entry conditions

AbstractThis study investigates a re-entry scenario of an Apollo-like space capsule with Direct Numerical Simulations (DNS). The simulation includes the chemical equilibrium gas model. Cross-flow-like vortices are induced through random distributed roughness patches on the capsule surface. Two different machine learning methods are used to predict the maximum vorticity magnitude downstream of a pseudo-random roughness patch, the wall-normal location of the vortex core and spanwise and wall-normal gradient maxima of u. A large DNS database is formed for training and testing of the neural networks. In order to understand the influence of the vorticity magnitude on the transition process, local one-dimensional inviscid (LODI) relations are used to describe perturbations at the inflow. The disturbance evolution in the streamwise direction is analysed with a two-dimensional Fourier transformation in time and space. We show how the vorticity magnitudes of the cross-flow-like vortices, spanwise and wall-normal derivatives of the streamwise velocity influence the transition location.

Improvement of low contrast images in the frequency domain using fuzzy intensification

Due to the variety of types of images, there are currently no universal methods that provide a guaranteed result of solving the problem of improving the quality of low-contrast digital images. Medical systems often produce images of insufficient quality for reliable visual analysis. In particular, X-ray images, characterized by low intensity, un-even background, high level of noise, poor contrast and weakly defined boundaries of structures, are particularly difficult to analyze and choose an effective processing meth-od. The paper presents the information possibilities of the method of processing half-tone medical images aimed at improving the contrast and increasing the detail of ob-jects of interest in order to increase the reliability of diagnosis based on them. The pro-posed algorithm is based on a multi-stage processing process, which includes the use of two-dimensional frequency Fourier transformation and the method of fuzzy intensifica-tion in the spatial domain. The use of two-dimensional discrete Fourier transformation changes not the im-age, but the form of its representation, converting the output signal into its components of different frequencies and amplitudes. In this form, it is much easier to carry out filter-ing or amplification of individual components of the signal. Fuzzy set theory has the ability to quantitatively and qualitatively model problems related to uncertainty and imprecision, which are always present in digital images. Their presence is determined both by the features of the physical processes of image forming systems and by the stage of creating a digital image. The application of the proposed method provides improved contrast and increased detailing of objects of interest and affects the reliability of visual analysis. Only the ar-guments of complex Fourier transform coefficients can be corrected. The method of fuzzy intensification is used as a refinement for the second stage of frequency conversion. The effect of frequency conversion parameters on the detail of the resulting image was stud-ied. The results of the algorithm are presented on the example of real X-ray images.

Performance improvement of non-orthogonal multiple access with a 3D constellation and a 2D IFFT modulator.

In this paper, we propose a performance improvement of non-orthogonal multiple access (NOMA) with a three-dimensional (3D) constellation and a two-dimensional Inverse Fast Fourier Transform IFFT modulator (2D-IFFT) for the passive optical network (PON). Two kinds of 3D constellation mapping are designed for the generation of a three-dimensional NOMA (3D-NOMA) signal. Higher-order 3D modulation signals can be obtained by superimposing signals of different power levels by pair mapping. Successive interference cancellation (SIC) algorithm is implemented at the receiver to remove interference from different users. Compared with the traditional two-dimensional NOMA (2D-NOMA), the proposed 3D-NOMA can increase the minimum Euclidean distance (MED) of constellation points by 15.48%, which enhances the bit error rate (BER) performance of the NOMA. The peak-to-average power ratio (PAPR) of NOMA can be reduced by 2 dB. A 12.17 Gb/s 3D-NOMA transmission over 25 km single-mode fiber (SMF) is experimentally demonstrated. The results show that at the bit error rate (BER) of 3.8 × 10-3, the sensitivity gain of the high-power signals of the two proposed 3D-NOMA schemes is 0.7 dB and 1 dB compared with that of 2D-NOMA under the condition of the same rate. Low-power level signal also has 0.3 dB and 1 dB performance improvement. Compared with 3D orthogonal frequency-division multiplexing (3D-OFDM), the proposed 3D-NOMA scheme could potentially expand the number of users without obvious performance degradation. Due to its good performance, 3D-NOMA is a potential method for future optical access systems.

Windowed Two-Dimensional Fourier Transform Concentration and Its Application to ISAR Imaging.

This paper presents a novel non-parametric technique for two-dimensional spectrum readability enhancement. The approach is based on relocating a windowed bivariate Fourier transform with regard to its frequency estimates computed using a moving analyzing window. To this aim, four spatial instantaneous frequency estimators are proposed. A strongly concentrated spectrum with improved component separability is obtained with the proposed technique. The method was intensively tested using simulated and real-life signals. As an example of the method application, inverse synthetic aperture radar (ISAR) images were created and then focused, significantly improving the contrast and entropy. However, the presented technique can be applied to other bivariate signal analyses whenever the windowed two-dimensional Fourier transform (W2D-FT) is applied.

Low Complexity Radar Gesture Recognition Using Synthetic Training Data

Developments in radio detection and ranging (radar) technology have made hand gesture recognition feasible. In heat map-based gesture recognition, feature images have a large size and require complex neural networks to extract information. Machine learning methods typically require large amounts of data and collecting hand gestures with radar is time- and energy-consuming. Therefore, a low computational complexity algorithm for hand gesture recognition based on a frequency-modulated continuous-wave (FMCW) radar and a synthetic hand gesture feature generator are proposed. In the low computational complexity algorithm, two-dimensional Fast Fourier Transform is implemented on the radar raw data to generate a range-Doppler matrix. After that, background modelling is applied to separate the dynamic object and the static background. Then a bin with the highest magnitude in the range-Doppler matrix is selected to locate the target and obtain its range and velocity. The bins at this location along the dimension of the antenna can be utilised to calculate the angle of the target using Fourier beam steering. In the synthetic generator, the Blender software is used to generate different hand gestures and trajectories and then the range, velocity and angle of targets are extracted directly from the trajectory. The experimental results demonstrate that the average recognition accuracy of the model on the test set can reach 89.13% when the synthetic data are used as the training set and the real data are used as the test set. This indicates that the generation of synthetic data can make a meaningful contribution in the pre-training phase.

Photoacoustic imaging a PDT response marker for monitoring vasculature changes

Photoacoustic imaging (PAI) is an evolving modality for studying and imaging tumor hypoxia. The experimental results from animals treated with ALA for Pre-PDT, Post-PDT, 4hr PDT, 24 hr PDT show a short-term increase in the BV followed by a strong decrease; however, no complete stasis. An alternate method is created by looking at the spatial and frequency domain histogram to observe the tumor vasculature. The images are represented in frequency domains by application of two-dimensional Fast Fourier Transform (FFT) on spatial domain images. The variations in acoustic impedance after Photodynamic Therapy (PDT) are studied. The photoacoustic signals implemented on tumor models indicated PDT influenced variations in the hemoglobin levels against different time periods and studied their outcome on the tumor necrosis.

Spirality: A Novel Way to Measure Spiral Arm Pitch Angle

We present the MATLAB code Spirality, a novel method for measuring spiral arm pitch angles by fitting galaxy images to spiral templates of known pitch. Computation time is typically on the order of 2 min per galaxy, assuming 8 GB of working memory. We tested the code using 117 synthetic spiral images with known pitches, varying both the spiral properties and the input parameters. The code yielded correct results for all synthetic spirals with galaxy-like properties. We also compared the code’s results to two-dimensional Fast Fourier Transform (2DFFT) measurements for the sample of nearby galaxies defined by DMS PPak. Spirality’s error bars overlapped 2DFFT’s error bars for 26 of the 30 galaxies. The two methods’ agreement correlates strongly with galaxy radius in pixels and also with i-band magnitude, but not with redshift, a result that is consistent with at least some galaxies’ spiral structure being fully formed by z=1.2, beyond which there are few galaxies in our sample. The Spirality code package also includes GenSpiral, which produces FITS images of synthetic spirals, and SpiralArmCount, which uses a one-dimensional Fast Fourier Transform to count the spiral arms of a galaxy after its pitch is determined. All code is freely available.