Fourier Transform Method Research Articles

Recognition of Persian Sign Language Alphabet Using Gaussian Distribution, Radial Distance and Centroid-Radii

Aims: Presenting a novel approach to identify Persian static symptoms in that the proposed sign language recognition system consists of two segmentation and feature extraction phases. In the segmentation phase, the hand region is separated by an effective segmentation method from the original image. Objective: (1) Introducing an effective framework to solve sensitivity to light conditions in identifying and recognizing letters of the Persian sign language alphabet. (2) Proposing a new feature extraction method to eliminate sensitivity to rotation and scale changes. (3) Creating a new dataset includes 480 images of the sign language alphabet symptoms in order to show the performance of our method. Methods: The proposed sign language recognition system uses two segmentation and feature extraction phases. In the segmentation phase, the hand region is separated by an effective segmentation method from the original image. This method is based on the unique Gaussian model in the YCbCr color space. The Bayes rule is used to precisely identify the hand region too. In the feature extraction phase, the radial model is used to obtain a one-dimensional function to display the hand region boundary and to compute the combined feature vector. In order to normalize this method, the Fourier Transformation method is applied. Results: The system was trained and tested using 480 image samples of Persian sign language characters, 15 images per sign, with the .jpg extension. Extensive experimental evaluations indicate that the proposed recognition system is less susceptible to displacement, scale, and rotation, and can detect symptoms at an accuracy of 95.62%. Conclusion: In this article, a new system was proposed for recognizing the alphabet letters in Persian sign language. This system consists of two main phases: the segmentation phase or the hand region identification and feature extraction phase. In the segmentation phase of the detection system, at first, the hand region is separated by an effective segmentation method from the original image. This method is based on the single Gaussian model in the color space of the YCbCr and the Bayes rule. Applying this method in hand segmentation, enables the system, to recognize the hand region well. In this method, after hand region detection, using the Sobel edge detector, the image edge is extracted. In the feature extraction phase, the radial distance model was used to obtain a one-dimensional function display of the hand region boundary and compute its feature vector. This model is based on the edge and image centroid and computes the centroid distance to the shape boundary as a function of the angle. Since this model by itself is sensitive to the scale variations and tilt, in order to normalize this method to tilt variations, the Fourier transformation was applied to feature vector computed by the radial model. Then the vector elements are divided by the largest vector element, thus, using this method the computed feature vector will be distinct for different images and will show less sensitivity to displacement, scale, and gradient. A database consist of 480 images of Persian sign symptoms was created to the overall accuracy evaluation of the system, the results show that the proposed recognition system can identify 32 letters of the Persian sign language alphabet with a detection rate 95.62%.

A Novel 3-D-NUFFT Method for the Efficient Calculation of the Array Factor of Conformal Arrays

A novel 3-D nonuniform Fourier transformation (3-D-NUFFT) method is proposed for the efficient calculation of the array factors of conformal arrays. Interpolation in a least-squares sense is first used to interpolate the topological structure of conformal arrays into that of uniformly spaced volumetric arrays. By applying the equivalent mathematical relationship between the 3-D discrete Fourier transform (DFT) and the array factor of the uniform volumetric arrays, the 3-D-FFT is then developed to calculate the array factor of uniformly spaced volumetric arrays. Therefore, the array factor of conformal arrays can be easily calculated according to the interpolation relationship between the conformal arrays and the uniform volumetric arrays. Representative numerical examples regarding the array factor calculation of spherical arrays with different excitations are provided. In comparison with the direct calculation method, the obtained results confirm the advantages and effectiveness of the proposed method.

Improving the Performance of Steel Machining Processes through Cutting by Vibration Control.

Machining processes through cutting are accompanied by dynamic phenomena that influence the quality of the processed surfaces. Thus, this research aimed to design, make, and use a tool with optimal functional geometry, which allowed a reduction of the dynamic phenomena that occur in the cutting process. In order to carry out the research, the process of cutting by front turning with transversal advance was taken into account. Additionally, semi-finished products with a diameter of Ø = 150 mm made of C45 steel were chosen for processing (1.0503). The manufacturing processes were performed with the help of two tools: a cutting tool, the classic construction version, and another that was the improved construction version. In the first stage of the research, an analysis was made of the vibrations that appear in the cutting process when using the two types of tools. Vibration analysis considered the following: use of the Fast Fourier Transform (FFT) method, application of the Short-Time Fourier-Transformation (STFT) method, and observation of the acceleration of vibrations recorded during processing. After the vibration analysis, the roughness of the surfaces was measured and the parameter Ra was taken into account, but a series of diagrams were also drawn regarding the curved profiles, filtered profiles, and Abbott–Firestone curve. The research showed that use of the tool that is the improved constructive variant allows accentuated reduction of vibrations correlated with an improvement of the quality of the processed surfaces.

Cosine Willow Tree Structure under Lévy Processes with Application to Pricing Variance Derivatives

Lévy process models can capture the large price changes on sudden exogenous events and can better demonstrate the high peak and heavy tail characteristics of financial data. The Fourier transformation method is famous for pricing derivatives under the Lévy processes beause of its efficiency, how it separates models from payoff function, and how it handles models with characteristic functions, but it is criticized for its restriction on path dependency. In this article, we propose a unified cosine willow tree method, which inherits the merits of the transformation method but overcomes its shortcomings. Moreover, the hedging Greeks can be obtained as a by-product from the tree structure with minor extra cost. Some popular variance derivatives are also discussed to demonstrate the flexibility of the proposed method in handling path dependency. Finally, the theoretical convergence is analyzed for various Lévy process models.

Determination of body waves quality factor in the NW Iran, with power spectrum analysis

As one of the ways to identify seismological characteristics in the region, determining the quality factor of seismic mapping can provide valuable information about inside the earth. This study investigates local site effects as a function of frequency and presents a new relationship for determining the quality factor in northwestern Iran with regard to local site effects. These maps are selected so that their signal-to-noise ratio (SNR) is greater than 5. This study uses the Short-Time Fourier Transform (STFT) method in which a fixed time window and its multiplication by a given signal are used. The coefficients resulting from this transformation are considered as wave amplitudes at any frequency by performing a short-time Fourier transform. The amount of power spectrum decay is used instead of the ground displacement amplitude decay. Since the number of samples will be different at different intervals and this makes it difficult to perform our analysis, the sample mean, presented as the power spectrum, was used. Local site effects and kappa, a function of the path and site effects, were investigated and became the basis of spectral decay calculations. The results of this study were compared with those of the previous work based on conventional and classical methods and the accuracy of the methods was evaluated using standard deviation (SD) values. Finally, the quality factor equations were obtained for the North-South component (N-S) as Q(f)=(78±2)f^((1.37±0.02)), for the East-West component (E-W) as Q(f)=(62±2)f^((1.5±0.03)), and for the vertical component (Z) as Q(f)=(87±2)f^((1.29±0.03)).

The SINC way: a fast and accurate approach to Fourier pricing

The goal of this paper is to investigate the method outlined by one of us (P. R.) in Cherubini, U., Della Lunga, G., Mulinacci, S. and Rossi, P. [Fourier Transform Methods in Finance, 2009 (John Wiley & Sons Inc.).] to compute option prices. We name it the SINC approach. While the COS method by Fang, F. and Oosterlee, C.W. [A novel pricing method for european options based on Fourier-cosine series expansions. SIAM. J. Sci. Comput., 2009, 31(2), 826–848.] leverages the Fourier-cosine expansion of truncated densities, the SINC approach builds on the Shannon Sampling Theorem revisited for functions with bounded support. We provide several results which were missing in the early derivation: (i) a rigorous proof of the convergence of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases; (ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothing options; (iii) a systematic comparison with the COS formula for several log-price models; iv) a numerical challenge against alternative Fast Fourier specifications, such as Carr, P. and Madan, D. [Option valuation using the fast Fourier transform. J. Comput. Finance, 1999, 2(4), 61–73.] and Lewis, A.L. [Option Valuation Under Stochastic Volatility with Mathematica Code, 2000 (Newport Beach: Finance Press).]; (v) an extensive pricing exercise under the rough Heston model of Jaisson, T. and Rosenbaum, M. [Limit theorems for nearly unstable Hawkes processes. Ann. Appl. Probab., 2015, 25(2), 600–631.]; (vi) formulas to evaluate numerically the moments of a truncated density. The advantages of the SINC approach are numerous. When compared to benchmark methodologies, SINC provides the most accurate and fast pricing computation. The method naturally lends itself to price all options in a smile concurrently by means of Fast Fourier techniques, boosting fast calibration. Pricing requires resorting only to odd moments in the Fourier space.

Dynamics of non-uniform breathing solitons of pulses in multimode fibers

We investigate the dynamics of non-uniform breathing solitons in multimode fibers modeled by the oscillating nonlinearities. By using the split-step Fourier-transform method to solve the nonlinear Schrödinger equation with the oscillating nonlinear coefficient, the evolution of non-uniform breathing solitons with irregular breathing periods in the multimode fiber is revealed under the action of second-order dispersion. Further, the number and depth of non-uniform breathers can be manipulated by adjusting the power of the pulse and the oscillation frequency of the nonlinear coefficient. Moreover, we also discuss the evolution of breathers under different dispersion conditions. Our study benefits for the better understanding of the complex dynamics of breathing solitons in multimode fibers.

Detection of COVID-19 findings by the local interpretable model-agnostic explanations method of types-based activations extracted from CNNs

Covid-19 is a disease that affects the upper and lower respiratory tract and has fatal consequences in individuals. Early diagnosis of COVID-19 disease is important. Datasets used in this study were collected from hospitals in Istanbul. The first dataset consists of COVID-19, viral pneumonia, and bacterial pneumonia types. The second dataset consists of the following findings of COVID-19: ground glass opacity, ground glass opacity, and nodule, crazy paving pattern, consolidation, consolidation, and ground glass. The approach suggested in this paper is based on artificial intelligence. The proposed approach consists of three steps. As a first step, preprocessing was applied and, in this step, the Fourier Transform and Gradient-weighted Class Activation Mapping methods were applied to the input images together. In the second step, type-based activation sets were created with three different ResNet models before the Softmax method. In the third step, the best type-based activations were selected among the CNN models using the local interpretable model-agnostic explanations method and re-classified with the Softmax method. An overall accuracy success of 99.15% was achieved with the proposed approach in the dataset containing three types of image sets. In the dataset consisting of COVID-19 findings, an overall accuracy success of 99.62% was achieved with the recommended approach.

Numerical methodology for simulating particle deposition on superhydrophobic surfaces with randomly distributed rough structures

Superhydrophobic coatings with a rough structure and low surface energy have been regarded as new high-efficiency anti-dust solutions. However, current research on the anti-dust mechanism of superhydrophobic materials is still insufficient. Main obstacles are the difficulty in determining the contact state between the dust particle and the rough structure and calculating the contact force accurately. Herein, a new methodology that introduces rough surface discretization and extends the Johnson-Kendall-Roberts (JKR) model to solve the adhesive contact forces of a particle-rough surface was proposed. Further, the lattice Boltzmann method coupled with the JKR-based discrete element method was employed to study the particle deposition characteristics on superhydrophobic surfaces with randomly distributed rough structures. Surfaces with different rough structures were reconstructed using the fast Fourier transformation method. The particle-airflow and rough surface-airflow interactions were calculated using the immersed moving boundary method. The coupling models and computation scheme were validated by comparing the simulation results with those recorded by a high-speed camera. The effects of the particle diameter, airflow inlet velocity, surface energy, and surface structures (characterized by skewness, kurtosis and standard deviation) on particle migration, deposition morphology and deposition rate were compared and analyzed. The results indicate that smaller particles with larger velocities are less likely to be deposited on superhydrophobic surface. Increasing the surface energy of the rough surface can significantly enhance the particle deposition rate owing to the strong particle–surface adhesion force. Further, appropriate surface roughness can reduce particle–surface adhesion and particle energy dissipation during collision, thereby leading to a deposition reduction. However, excessive peaks and deep valleys on the rough surface would hinder the rolling and translation of the particles, thereby resulting in particle accumulation on the surface. Finally, using superhydrophobic surfaces with a skewness of 0 and kurtosis of approximately 5.0, and appropriately reducing the standard deviation of the rough-surface structures can significantly enhance the effect of superhydrophobic surfaces on anti-dust performance.

Classification of Women's Voices Using Fast Fourier Transform (FFT) Method

Everyone has a different kind of voice. Based on gender, voice type is divided into six parts, namely soprano, mezzo soprano, and alto for women; and tenor, baritone, and bass in men. Each type of sound has a different range and with different frequencies. This study classified the type of voice in women using the Fast Fourier Transform (FFT) method by recording the voices of each user which would then be processed using the FFT method to obtain the appropriate sound range. This research got results with an accuracy of up to 80%.The results obtained from this study are quite appropriate and it is proven that the FFT method can be used in digital signal processing.

Linking a phase field model for polymer crystallization to full-field micromechanical simulations of semi-crystalline polymers

An enhanced phase field model recently proposed by the authors enables to model polymer crystallization and to predict spherulite growth and representative semi-crystalline micro-structures in 2D or 3D. After solidification, the value of the phase field variable in each subcell (2D pixel or 3D voxel) indicates whether the material is amorphous or crystalline. In the present paper, full-field micromechanical simulations are conducted on the microstructures generated by the enhanced phase field model in order to predict the effective mechanical properties. A Fast Fourier Transform (FFT) method with periodic boundary conditions is used. Care is taken to obtain representative volume elements (RVEs) by computing the number of subcells in each spherulite and the number of spherulite nucleations in each RVE. Numerical FFT predictions of elastic properties for a range of crystallinity ratios are validated against experimental data and compared to simpler composite inclusion models. Finite element simulations of thermal shrinkage are also shown. The approach was numerically implemented in a research version of the Digimat software.

Observation of a different type of splitting solitons induced by interaction of second order spatial solitons

In this work the behavior of the split solitons derived from the interaction between two (1 + 1)- Dimensional second-order bright spatial solitons, is numerically investigated. Each individual interaction occurs when the two second-order solitons are initially propagating in the parallel way, while the variety of relative phases and the different initial transversal separation are adjusted. When the initial separation distance is on the appropriate distance where they feel the presence of other soliton, both second-order solitons breakup into a couple of first order (fundamental) low- and high-amplitude solitons, and consequently their initial parallel path suffers a lot. Although the propagation path of high- amplitude solitons receive low effects due to interaction and consequently almost follow their initial propagation path, the propagation path of the low-amplitude solitons suffers based on their initial relative phase. The derived low-amplitude fundamental solitons interact with each other and their propagation path also, as usual of their basic interaction properties, while the high-amplitude fundamental solitons, do not show the interaction, and almost continue their own parallel paths. As the initial separation distance decreases, and almost the initial overlap occurs, the propagation paths suffer for both (high and low amplitude) fundamental solitons. Behavior of the broken solitons induced by the interaction between the second order spatial solitons are investigated by solving the Nonlinear Schrodinger equation (NLSE), and it is simulated numerically by MATLAB program by using the well-known Split-Step Fourier Transform method.

GS-FrFT Algorithmic Method for Measurement of CD in Fibre Optics

The migration of present data network to the IoT interface, witty utilization of huge liable Single Mode Fiber rather than re-installing the whole network with Dispersion Shifted Fiber for their upgrading to ultra data speed Optical Fiber System based MPLS network for countering the main impediment of Chromatic Dispersion by estimating the real foe and compensating it at the receiver end and hence results the system more efficient with the existing Fiber network. The present scanning method of Fractional Fourier Transform (FrFT) to measure the Chromatic Dispersion (CD) encounters constraints of high latency time along with worst dispersion estimation error 250 picoseconds/nanometre which can be drastically improved with Golden Scan Search (GS) FrFT based algorithm method with 5 to 6 sec latency time and estimation error improved and obtained less than 80 picoseconds/nanometre.

Robust attitude estimation of rotating space debris based on virtual observations of neural network

SummaryHigh precise estimation and prediction of the target's attitude motion are key technologies for capturing and removing rotating space debris. In this article, a neural‐network‐enhanced Kalman filter (NNEKF) is proposed to improve the precision and robustness of attitude estimation algorithm. The main innovation of the NNEKF is to utilize virtual observations of the inertia characteristics to improve the filter's performances. The virtual observations are obtained using a neural network, which is offline trained using simulation data. In order to decrease the number of nodes of the network, the input data are preprocessed using the discrete Fourier transformation method. Moreover, by involving the characteristic frequencies in the input vector, the neural network can extract information from all the past observations, so as to grasp long‐term characteristics of the dynamical system. Therefore, the NNEKF can provide more precise estimation of the target's moment of inertia, and furthermore improve the accuracy and robustness of attitude estimation and prediction. Simulation results indicate that the NNEKF can reduce the estimation errors by 39% compared with the conventional EKF method when using the same measurement data. And the accumulation errors of prediction using estimates of the NNEKF is just as 24% as the conventional EKF.

On Combining with Fourier Transform and Adomian Methods to solve the Riccati Equations

In this paper, we apply the Fourier transform method with the Adomian decomposition method to solve Riccati equations . Proposed method is based on the Fourier transform and adomian decomposition methods. The solutions obtained using FADMs are compared with the numerical solutions obtained using the Rung Kutta2 and Euler method. Also, error graphs of the solutions are presented.

Comparison between Vortex-In-Cell and Vortex Particle Methods on Two-Dimensional Problem

This research is concerned with the two-dimensional vortex method (VM) solvers. We develop and investigate the performance of the Vortex-In-Cell (VIC) and Vortex Particle Method (VPM) which are well known as the VM’s family members. The advantage of these both methods are that we can accelerate velocity computation procedure, an N-body problem in numerical methods, by using Fast Fourier Transform (FFT) and Fast Multipole Method (FMM), respectively. In addition, the viscous calculation process in VPM can be accelerated by using a scheme of Nearest Neighbor Particle Searching (NNPS) algorithms. Moreover, the no-through boundary condition treatment issue can be easily handled by using an immersed boundary condition for both methods. The accuracy and numerical cost of both numerical methods will be examined by simulating flow over an Impulsively Started Circular Cylinder and comparisons

Transform-based phase retrieval techniques from a single off-axis interferogram

Optical phase retrieval (OPR) methods are important because they are used to obtain the transverse phase profile information of a beam. Interference methods are extensively used to convert the phase information into an intensity pattern, which can then be processed further to retrieve the unknown phase. The most widely used interference method involves the interference of the unknown object beam and a known reference beam with an angle between them. There are several algorithms that retrieve the phase information from such a single off-axis interference pattern. For a particular application, the choice of an algorithm for OPR is very important. Therefore, it is necessary to choose between them, depending on the requirements. Three entirely different noniterative, transform-based algorithms, namely the Fourier transform (FT) method, the continuous wavelet transform (CWT) method, and the Hilbert transform (CWT) method, are explained in detail. A quantitative comparison is made using a combination of rms error and standard structural similarity measure. The advantages of using a standard unwrapping algorithm are also validated using the same combination of comparison metrics. We show that the HT method has a better response with object beam with higher spatial frequency content, but with the penalty of affected noise. The FT method and CWT method have better noise immunity, but have the limitation of the spatial frequency range of the object beam. The different constraints, advantages, and some practical limitations of the methods are discussed with the help of a quantitative phase imaging experiment of monodispersed polymethyl methacrylate beads.

Fast generation of 360-degree cylindrical photorealistic hologram using ray-optics based methods.

Due to the large pixel pitch and limited size of spatial light modulator (SLM), the field of view (FOV) of current holographic display is greatly restricted. Cylindrical holography can effectively overcome the constraints of FOV. However, the existent algorithms of cylindrical hologram are all based on the wave-optics based approach. In this paper, to the best of our knowledge, we adopt the ray-optics based approach in the generation of cylindrical computer generated hologram (CCGH) for the first time. Information of parallax images captured from three-dimensional (3D) objects using a curved camera array is recorded into a cylindrical hologram. Two different recording specific algorithms are proposed, one is based on the Fast Fourier Transform (FFT) method, and another is based on the pinhole-type integral imaging (PII) method. The simulation results confirm that our proposed methods are able to realize a fast generation of the cylindrical photorealistic hologram.

FRICTIONAL EFFECTS ON THE DYNAMIC RESPONSES OF A SINGLE-STAGE SPUR GEAR SYSTEMS

Gears are paramout rotary mechanical equipment as its used in many industrial applications, for example in cars, industrial compressors and other applications. Therefore, monitoring the development of its condition is very important to prevent the aggravation of defects and stopping production. Friction between gears is causes of vibration but its representation in modeling and the analysis of its effect on the dynamic response is a very complex matter. In this study, the friction effect was studied by relying on equal load sharing formula and by relying on the sliding velocity direction of single-stage spur gears. The time domain was converted to the frequency domain, depending on the Fast Fourier Transform ( FFT ) method. Dynamic modeling results indicate that the friction between gears has a significant effect on the Vibration response of gearbox. This effect can be noticed by increasing the vibration amplitude in the time domain. It can also be seen by increasing the gear mesh frequency (GMF) amplitude and by increasing the amplitude of its harmonics in the frequency domain.

Fourier transformation method for some types of nonlinear partial differential equations

Предлагается метод анализа задачи Коши для широкого класса уравнений со степенными нелинейностями. В основе метода лежит преобразование Фурье, позволяющее свести исходное уравнение к интегро-дифференциальному. Доказано существование решений.