Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption ev...Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption events,and conducting space weather forecasting.This study aims to explore the effective use of radioheliographs for solar observations,specifically for imaging coronal mass ejections(CME),to track their evolution and provide space weather warnings.We have developed an imaging simulation program based on the principle of aperture synthesis imaging,covering the entire data processing flow from antenna configuration to dirty map generation.For grid processing,we propose an improved non-uniform fast Fourier transform(NUFFT)method to provide superior image quality.Using simulated imaging of radio coronal mass ejections,we provide practical recommendations for the performance of radioheliographs.This study provides important support for the validation and calibration of radioheliograph data processing,and is expected to profoundly enhance our understanding of solar activities.展开更多
Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properti...Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.展开更多
This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic d...This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.展开更多
This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a ...This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.展开更多
In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechani...In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.展开更多
Globally,economies have become complex and new technologies have transformed and facilitated the modernization of economies.In the previous literature,economic complexity approach has become one of the popular tools i...Globally,economies have become complex and new technologies have transformed and facilitated the modernization of economies.In the previous literature,economic complexity approach has become one of the popular tools in the development and innovation studies of economic geography.Researchers have found that green technology and eco-innovation approaches should be used to decisively reduce the effects of carbon emissions on the environment.However,debates about the impact of economic complexity on environment remain unsettled since some emerging production technologies have far-reaching pollution effects.This study explored the impacts of economic complexity on environmental sustainability in Turkey using the novel Fourier-based approaches,namely:Fourier Augmented Dickey-Fuller(FADF)and Fourier Autoregressive-Distributed Lag(FARDL)models.The Fourier-based approaches indicated that all variables(economic complexity index(ECI),GDP,energy consumption,and CO_(2)emission(CO_(2)E))are cointegrated in the long run.Additionally,the FARDL model implied that(i)in the long run,the effect of ECI(as a proxy for economic complexity),GDP(as a proxy for economic growth),and energy consumption on CO_(2)E(as a proxy for environmental quality)are important;(ii)economic complexity decreases environmental degradation in Turkey;and(iii)economic growth and energy consumption negatively affect environmental quality.The results also showed that economic complexity could be used as a policy tool to tackle environmental degradation.The findings also revealed that the fossil fuelbased economy will continue to expand and undermine Turkey’s efforts to meet its net zero emission target by 2053.Therefore,policy-makers should take actions and establish diversified economic,environmental,and energy strategies.For policy insights,the Turkish governments can use the combination of tax exemptions and technical support systems to support knowledge creation and the diffusion of environmentally friendly technologies The governments can also impose strict environmental regulations on the knowledge development phases.展开更多
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourie...This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.展开更多
We propose a method of complex-amplitude Fourier single-pixel imaging(CFSI)with coherent structured illumination to acquire both the amplitude and phase of an object.In the proposed method,an object is illustrated by ...We propose a method of complex-amplitude Fourier single-pixel imaging(CFSI)with coherent structured illumination to acquire both the amplitude and phase of an object.In the proposed method,an object is illustrated by a series of coherent structured light fields,which are generated by a phase-only spatial light modulator,the complex Fourier spectrum of the object can be acquired sequentially by a single-pixel photodetector.Then the desired complex-amplitude image can be retrieved directly by applying an inverse Fourier transform.We experimentally implemented this CFSI with several different types of objects.The experimental results show that the proposed method provides a promising complex-amplitude imaging approach with high quality and a stable configuration.Thus,it might find broad applications in optical metrology and biomedical science.展开更多
This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafuncti...This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafunctions and the Ishigami function are considered in the sensitivity analysis(SA).The effects of the input variables on the output variables are investigated,and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.展开更多
基金supported by the grants of National Natural Science Foundation of China(42374219,42127804)the Qilu Young Researcher Project of Shandong University.
文摘Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption events,and conducting space weather forecasting.This study aims to explore the effective use of radioheliographs for solar observations,specifically for imaging coronal mass ejections(CME),to track their evolution and provide space weather warnings.We have developed an imaging simulation program based on the principle of aperture synthesis imaging,covering the entire data processing flow from antenna configuration to dirty map generation.For grid processing,we propose an improved non-uniform fast Fourier transform(NUFFT)method to provide superior image quality.Using simulated imaging of radio coronal mass ejections,we provide practical recommendations for the performance of radioheliographs.This study provides important support for the validation and calibration of radioheliograph data processing,and is expected to profoundly enhance our understanding of solar activities.
文摘Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.
文摘This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.
文摘This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents at the College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.
文摘Globally,economies have become complex and new technologies have transformed and facilitated the modernization of economies.In the previous literature,economic complexity approach has become one of the popular tools in the development and innovation studies of economic geography.Researchers have found that green technology and eco-innovation approaches should be used to decisively reduce the effects of carbon emissions on the environment.However,debates about the impact of economic complexity on environment remain unsettled since some emerging production technologies have far-reaching pollution effects.This study explored the impacts of economic complexity on environmental sustainability in Turkey using the novel Fourier-based approaches,namely:Fourier Augmented Dickey-Fuller(FADF)and Fourier Autoregressive-Distributed Lag(FARDL)models.The Fourier-based approaches indicated that all variables(economic complexity index(ECI),GDP,energy consumption,and CO_(2)emission(CO_(2)E))are cointegrated in the long run.Additionally,the FARDL model implied that(i)in the long run,the effect of ECI(as a proxy for economic complexity),GDP(as a proxy for economic growth),and energy consumption on CO_(2)E(as a proxy for environmental quality)are important;(ii)economic complexity decreases environmental degradation in Turkey;and(iii)economic growth and energy consumption negatively affect environmental quality.The results also showed that economic complexity could be used as a policy tool to tackle environmental degradation.The findings also revealed that the fossil fuelbased economy will continue to expand and undermine Turkey’s efforts to meet its net zero emission target by 2053.Therefore,policy-makers should take actions and establish diversified economic,environmental,and energy strategies.For policy insights,the Turkish governments can use the combination of tax exemptions and technical support systems to support knowledge creation and the diffusion of environmentally friendly technologies The governments can also impose strict environmental regulations on the knowledge development phases.
基金supported by the Deanship of Scientific Research at King Khalid University,Saudi Arabia (R.G.P.1/207/43)。
文摘This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.
基金Project supported by the Natural Science Foundation of Hebei Province,China(Grant Nos.A2022201039 and F2019201446)the MultiYear Research Grant of University of Macao,China(Grant No.MYRG2020-00082-IAPME)+2 种基金the Science and Technology Development Fund from Macao SAR(FDCT),China(Grant No.0062/2020/AMJ)the Advanced Talents Incubation Program of the Hebei University(Grant No.8012605)the National Natural Science Foundation of China(Grant Nos.11204062,61774053,and 11674273)。
文摘We propose a method of complex-amplitude Fourier single-pixel imaging(CFSI)with coherent structured illumination to acquire both the amplitude and phase of an object.In the proposed method,an object is illustrated by a series of coherent structured light fields,which are generated by a phase-only spatial light modulator,the complex Fourier spectrum of the object can be acquired sequentially by a single-pixel photodetector.Then the desired complex-amplitude image can be retrieved directly by applying an inverse Fourier transform.We experimentally implemented this CFSI with several different types of objects.The experimental results show that the proposed method provides a promising complex-amplitude imaging approach with high quality and a stable configuration.Thus,it might find broad applications in optical metrology and biomedical science.
文摘This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafunctions and the Ishigami function are considered in the sensitivity analysis(SA).The effects of the input variables on the output variables are investigated,and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.
