The single-pixel imaging(SPI) technique is able to capture two-dimensional(2 D) images without conventional array sensors by using a photodiode. As a novel scheme, Fourier single-pixel imaging(FSI) has been proven cap...The single-pixel imaging(SPI) technique is able to capture two-dimensional(2 D) images without conventional array sensors by using a photodiode. As a novel scheme, Fourier single-pixel imaging(FSI) has been proven capable of reconstructing high-quality images. Due to the fact that the Fourier basis patterns(also known as grayscale sinusoidal patterns)cannot be well displayed on the digital micromirror device(DMD), a fast FSI system is proposed to solve this problem by binarizing Fourier pattern through a dithering algorithm. However, the traditional dithering algorithm leads to low quality as the extra noise is inevitably induced in the reconstructed images. In this paper, we report a better dithering algorithm to binarize Fourier pattern, which utilizes the Sierra–Lite kernel function by a serpentine scanning method. Numerical simulation and experiment demonstrate that the proposed algorithm is able to achieve higher quality under different sampling ratios.展开更多
In this paper, the generalized nonlinear Schrodinger equation (GNLSE) is solved by an adaptive split-step Fourier method (ASSFM). It is found that ASSFM must be used to solve GNLSE to ensure precision when the sol...In this paper, the generalized nonlinear Schrodinger equation (GNLSE) is solved by an adaptive split-step Fourier method (ASSFM). It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre (PCF) parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.展开更多
To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals,a novel kind of anti-aliasing algorithm based on the short time Fourier transform(STFT)is brought forward.First ...To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals,a novel kind of anti-aliasing algorithm based on the short time Fourier transform(STFT)is brought forward.First the physical essence of aliasing that occurs is analyzed;second the interpolation algorithm model is setup based on the Hamming window;then the fast implementation of the algorithm using the Newton iteration method is given.Using the numerical simulation the feasibility of algorithm is validated.Finally,the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.展开更多
On the basis of high precision requirement for input signals in the power system protection and control system,this paper,only for the influence of power system frequency deviation on extracting fundamental harmonic,s...On the basis of high precision requirement for input signals in the power system protection and control system,this paper,only for the influence of power system frequency deviation on extracting fundamental harmonic,studies the amplitude error of Fourier algorithm,presents a method of correcting frequency deviation,and further derives the formulas of improved Fourier algorithm.The simulation results verified the effectiveness of the algorithm,it not only can greatly weaken the influence of frequency deviation,but also increase the precision of the power system protection and control.As a result the study in this paper has practical application value.展开更多
In order to improve femtosecond laser throughput,a parallel processing system consisting of liquid crystal on silicon(LCOS)device as spatial light modulator is put forward.A method is described for displaying Fourier ...In order to improve femtosecond laser throughput,a parallel processing system consisting of liquid crystal on silicon(LCOS)device as spatial light modulator is put forward.A method is described for displaying Fourier hologram on LCOS,and a high uniformity of several diffraction peaks in the computer reconstruction is achieved.Application of this method to the parallel femtosecond laser processing is also demonstrated,and two intersecting rings and three tangent rings are fabricated respectively by one time in the photoresist.展开更多
The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transf...The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transform.Then,using the Fourier transform and its inverse,we derive the analytical pricing formulas of power options which are expressed in the form of Fourier integral.In addition,the fast Fourier transform(FFT)algorithm is applied to calculate these pricing formulas.Finally,Shangzheng 50ETF options are chosen to test our results.Estimating the parameters in NIG process by maximum likelihood method,we show that the NIG prices are much closer to market prices than the Black-Scholes-Merton(BSM)ones.展开更多
In this paper, an approximate analytical algorithm in the form of direct Fourier reconstruction is obtained for the recon- struction of data functions arisen from ^-scheme short-scan sin- gle-photon emission computed ...In this paper, an approximate analytical algorithm in the form of direct Fourier reconstruction is obtained for the recon- struction of data functions arisen from ^-scheme short-scan sin- gle-photon emission computed tomography(SPECT) with uniform attenuation, and the modified central slice theorem is developed. Numerical simulations are conducted to demonstrate the effec- tiveness of the developed method.展开更多
In the paper,a reduced basis(RB)method for time-dependent nonlocal problems with a special parameterized fractional Laplace kernel function is proposed.Because of the lack of sparsity of discretized nonlocal systems c...In the paper,a reduced basis(RB)method for time-dependent nonlocal problems with a special parameterized fractional Laplace kernel function is proposed.Because of the lack of sparsity of discretized nonlocal systems compared to corresponding local partial differential equation(PDE)systems,model reduction for nonlocal systems becomes more critical.The method of snapshots and greedy(MOS-greedy)algorithm of RB method is developed for nonlocal problems with random inputs,which provides an efficient and reliable approximation of the solution.A major challenge lies in the excessive influence of the time domain on the model reduction process.To address this,the Fourier transform is applied to convert the original time-dependent parabolic equation into a frequency-dependent elliptic equation,where variable frequencies are independent.This enables parallel computation for approximating the solution in the frequency domain.Finally,the proposed MOS-greedy algorithm is applied to the nonlocal diffusion problems.Numerical results demonstrate that it provides an accurate approximation of the full order problems and significantly improves computational efficiency.展开更多
Color Fourier single-pixel imaging(FSI)enables efficient spectral and spatial imaging.Here,we propose a Fourier single-pixel imaging scheme with a random color filter array(FSI-RCFA).The proposed method employs a rand...Color Fourier single-pixel imaging(FSI)enables efficient spectral and spatial imaging.Here,we propose a Fourier single-pixel imaging scheme with a random color filter array(FSI-RCFA).The proposed method employs a random color filter array(RCFA)to modulate Fourier patterns.A three-step phase-shifting technique reconstructs the Fourier spectrum,followed by an RCFA-based demosaicing algorithm to recover color images.Compared to traditional color FSI based on Bayer color filter array schemes(FSI-BCFA),our approach achieves superior separation between chrominance and luminance components in the frequency domain.Simulation results demonstrate that the FSI-RCFA method achieves a lower mean squared error(MSE),a higher peak signal-to-noise ratio(PSNR),and superior noise resistance compared to FSI-BCFA,while enabling direct single-channel pixel measurements for targeted applications such as agricultural defect detection.展开更多
The Fourier series (FS) applies to a periodic non-sinusoidal function satisfying the Dirichlet conditions, whereas the being-processed function in practical applications is usually an aperiodic non-sinusoidal signal. ...The Fourier series (FS) applies to a periodic non-sinusoidal function satisfying the Dirichlet conditions, whereas the being-processed function in practical applications is usually an aperiodic non-sinusoidal signal. When is aperiodic, its calculated FS is not correct, which is still a challenging problem. To overcome the problem, we derive a direct calculation algorithm, a constant iteration algorithm, and an optimal iteration algorithm. The direct calculation algorithm correctly calculates its Fourier coefficients (FCs) when is periodic and satisfies the Dirichlet conditions. Both the constant iteration algorithm and the optimal iteration algorithm provide an idea of determining the states of . From the idea, we obtain an algorithm for determining the states of based on the optimal iteration algorithm. In the algorithm, the variable iteration step is introduced; thus, we present an algorithm for determining the states of based on the variable iteration step. The presented algorithm accurately determines the states of . On the basis of these algorithms, we build a biproportional construction theory. The theory consists of a first and a second proportional construction theory. The former correctly calculates the FCs of at the present sampling time展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61271376)the Anhui Provincial Natural Science Foundation,China(Grant No.1208085MF114)
摘要The single-pixel imaging(SPI) technique is able to capture two-dimensional(2 D) images without conventional array sensors by using a photodiode. As a novel scheme, Fourier single-pixel imaging(FSI) has been proven capable of reconstructing high-quality images. Due to the fact that the Fourier basis patterns(also known as grayscale sinusoidal patterns)cannot be well displayed on the digital micromirror device(DMD), a fast FSI system is proposed to solve this problem by binarizing Fourier pattern through a dithering algorithm. However, the traditional dithering algorithm leads to low quality as the extra noise is inevitably induced in the reconstructed images. In this paper, we report a better dithering algorithm to binarize Fourier pattern, which utilizes the Sierra–Lite kernel function by a serpentine scanning method. Numerical simulation and experiment demonstrate that the proposed algorithm is able to achieve higher quality under different sampling ratios.
摘要In this paper, the generalized nonlinear Schrodinger equation (GNLSE) is solved by an adaptive split-step Fourier method (ASSFM). It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre (PCF) parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.
基金the National Natural Science Foundation of China(9040700760372001).
摘要To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals,a novel kind of anti-aliasing algorithm based on the short time Fourier transform(STFT)is brought forward.First the physical essence of aliasing that occurs is analyzed;second the interpolation algorithm model is setup based on the Hamming window;then the fast implementation of the algorithm using the Newton iteration method is given.Using the numerical simulation the feasibility of algorithm is validated.Finally,the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.
摘要On the basis of high precision requirement for input signals in the power system protection and control system,this paper,only for the influence of power system frequency deviation on extracting fundamental harmonic,studies the amplitude error of Fourier algorithm,presents a method of correcting frequency deviation,and further derives the formulas of improved Fourier algorithm.The simulation results verified the effectiveness of the algorithm,it not only can greatly weaken the influence of frequency deviation,but also increase the precision of the power system protection and control.As a result the study in this paper has practical application value.
基金National Natural Science Foundation of China(No.51275502)Natural Science Key Project of Anhui Province(No.KJ2011A014)+1 种基金China Postdoctoral Science Foundation funded project(NO.2012M511416)The Innovation Foundationof Anhui University and the Personnel Construction Project of Anhui University
摘要In order to improve femtosecond laser throughput,a parallel processing system consisting of liquid crystal on silicon(LCOS)device as spatial light modulator is put forward.A method is described for displaying Fourier hologram on LCOS,and a high uniformity of several diffraction peaks in the computer reconstruction is achieved.Application of this method to the parallel femtosecond laser processing is also demonstrated,and two intersecting rings and three tangent rings are fabricated respectively by one time in the photoresist.
基金Supported by National Natural Science Foundation of China(11571089,11501164)Natural Science Founda-tion of Hebei Province(A2019205299)+1 种基金the Foundation of Hebei Education Department(ZD2018065,ZD2019053)Hebei Normal University(L2019Z01).
摘要The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transform.Then,using the Fourier transform and its inverse,we derive the analytical pricing formulas of power options which are expressed in the form of Fourier integral.In addition,the fast Fourier transform(FFT)algorithm is applied to calculate these pricing formulas.Finally,Shangzheng 50ETF options are chosen to test our results.Estimating the parameters in NIG process by maximum likelihood method,we show that the NIG prices are much closer to market prices than the Black-Scholes-Merton(BSM)ones.
基金Supported by the National Natural Science Foundation of China(61271398)the Natural Science Foundation of Ningbo(2012A610031)
摘要In this paper, an approximate analytical algorithm in the form of direct Fourier reconstruction is obtained for the recon- struction of data functions arisen from ^-scheme short-scan sin- gle-photon emission computed tomography(SPECT) with uniform attenuation, and the modified central slice theorem is developed. Numerical simulations are conducted to demonstrate the effec- tiveness of the developed method.
基金supported by the Guangdong Basic and Applied Basic Research Foundation,China(Grant 2024A1515012548)supported by the National Natural Science Foundation of China(Grant 12401567)+1 种基金by the 2023 Guangzhou Basic and Applied Basic Research Project(Grant 2023A04J0035)by the Talent Special Projects of School-level Scientific Research Programs under Guangdong Poiytechnic Normal University(Grant 2022SDKYA025).
摘要In the paper,a reduced basis(RB)method for time-dependent nonlocal problems with a special parameterized fractional Laplace kernel function is proposed.Because of the lack of sparsity of discretized nonlocal systems compared to corresponding local partial differential equation(PDE)systems,model reduction for nonlocal systems becomes more critical.The method of snapshots and greedy(MOS-greedy)algorithm of RB method is developed for nonlocal problems with random inputs,which provides an efficient and reliable approximation of the solution.A major challenge lies in the excessive influence of the time domain on the model reduction process.To address this,the Fourier transform is applied to convert the original time-dependent parabolic equation into a frequency-dependent elliptic equation,where variable frequencies are independent.This enables parallel computation for approximating the solution in the frequency domain.Finally,the proposed MOS-greedy algorithm is applied to the nonlocal diffusion problems.Numerical results demonstrate that it provides an accurate approximation of the full order problems and significantly improves computational efficiency.
基金supported by the National Natural Science Foundation of China(Grant Nos.62001249 and62375140)。
摘要Color Fourier single-pixel imaging(FSI)enables efficient spectral and spatial imaging.Here,we propose a Fourier single-pixel imaging scheme with a random color filter array(FSI-RCFA).The proposed method employs a random color filter array(RCFA)to modulate Fourier patterns.A three-step phase-shifting technique reconstructs the Fourier spectrum,followed by an RCFA-based demosaicing algorithm to recover color images.Compared to traditional color FSI based on Bayer color filter array schemes(FSI-BCFA),our approach achieves superior separation between chrominance and luminance components in the frequency domain.Simulation results demonstrate that the FSI-RCFA method achieves a lower mean squared error(MSE),a higher peak signal-to-noise ratio(PSNR),and superior noise resistance compared to FSI-BCFA,while enabling direct single-channel pixel measurements for targeted applications such as agricultural defect detection.
摘要The Fourier series (FS) applies to a periodic non-sinusoidal function satisfying the Dirichlet conditions, whereas the being-processed function in practical applications is usually an aperiodic non-sinusoidal signal. When is aperiodic, its calculated FS is not correct, which is still a challenging problem. To overcome the problem, we derive a direct calculation algorithm, a constant iteration algorithm, and an optimal iteration algorithm. The direct calculation algorithm correctly calculates its Fourier coefficients (FCs) when is periodic and satisfies the Dirichlet conditions. Both the constant iteration algorithm and the optimal iteration algorithm provide an idea of determining the states of . From the idea, we obtain an algorithm for determining the states of based on the optimal iteration algorithm. In the algorithm, the variable iteration step is introduced; thus, we present an algorithm for determining the states of based on the variable iteration step. The presented algorithm accurately determines the states of . On the basis of these algorithms, we build a biproportional construction theory. The theory consists of a first and a second proportional construction theory. The former correctly calculates the FCs of at the present sampling time