An improved non-uniform fast Fourier transform method for radio imaging of coronal mass ejections

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.

Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

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.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

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.

Retrieval algorithm of quantitative analysis of passive Fourier transform infrared (FTRD) remote sensing measurements of chemical gas cloud from measuring the transmissivity by passive remote Fourier transform infrared

Passive Fourier transform infrared （FTIR） remote sensing measurement of chemical gas cloud is a vital technology. It takes an important part in many fields for the detection of released gases. The principle of concentration measurement is based on the Beer-Lambert law. Unlike the active measurement, for the passive remote sensing, in most cases, the difference between the temperature of the gas cloud and the brightness temperature of the background is usually a few kelvins. The gas cloud emission is almost equal to the background emission, thereby the emission of the gas cloud cannot be ignored. The concentration retrieval algorithm is quite different from the active measurement. In this paper, the concentration retrieval algorithm for the passive FTIR remote measurement of gas cloud is presented in detail, which involves radiative transfer model, radiometric calibration, absorption coefficient calculation, et al. The background spectrum has a broad feature, which is a slowly varying function of frequency. In this paper, the background spectrum is fitted with a polynomial by using the Levenberg-Marquardt method which is a kind of nonlinear least squares fitting algorithm. No background spectra are required. Thus, this method allows mobile, real-time and fast measurements of gas clouds.

The application of Fourier transform mid-infrared(FTIR) spectroscopy to identify variation in cell wall composition of Setaria italica ecotypes

Cell wall composition in monocotyledonous grasses has been identified as a key area of research for developing better feedstocks for forage and biofuel production.Setaria viridis and its close domesticated relative Setaria italica have been chosen as suitable monocotyledonous models for plants possessing the C4 pathway of photosynthesis including sorghum,maize,sugarcane,switchgrass and Miscanthus×giganteus.Accurate partial least squares regression（PLSR）models to predict S.italica stem composition have been generated,based upon Fourier transform mid-infrared（FTIR）spectra and calibrated with wet chemistry determinations of ground S.italica stem material measured using a modified version of the US National Renewable Energy Laboratory（NREL）acid hydrolysis protocol.The models facilitated a high-throughput screening analysis for glucan,xylan,Klason lignin and acid soluble lignin（ASL）in a collection of 183 natural S.italica variants and clustered them into classes,some possessing unique chemotypes.The predictive models provide a highly efficient screening tool for large scale breeding programs aimed at identifying lines or mutants possessing unique cell wall chemotypes.Genes encoding key catalytic enzymes of the lignin biosynthesis pathway exhibit a high level of conservation with matching expression profiles,measured by RT-q PCR,among accessions of S.italica,which closely mirror profiles observed in the different developmental regions of an elongating internode of S.viridis by RNASeq.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

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.

Quantum entangled fractional Fourier transform based on the IWOP technique

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.

From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation（FrST） which satisfies additivity.By virtue of the integration technique within the ordered product of operators（IWOP） we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa＋a/2 and exp[iα/2（a^2 ＋a^＋2）.The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.

Fourier and wavelet transformations application to fault detection of induction motor with stator current

Fault detection of an induction motor was carried out using the information of the stator current. After synchronizing the actual data, Fourier and wavelet transformations were adopted in order to obtain the sideband or detail value characteristics under healthy and various faulty operating conditions. The most reliable phase current among the three phase currents was selected using an approach that employs the fuzzy entropy measure. Data were trained with a neural network system, and the fault detection algorithm was verified using the unknown data. Results of the proposed approach based on Fourier and wavelet transformations indicate that the faults can be properly classified into six categories. The training error is 5.3×10-7, and the average test error is 0.103.

Dual Image Cryptosystem Using Henon Map and Discrete Fourier Transform

This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.

GP Algorithm-Based Fourier Transform Infrared Spectrum Trend Term Removal Model

Trend term removal is a key step in Fourier transform infrared spectroscopy(FTIR)data pre-processing.The most commonly used least squares(LS)method,although satisfying the real-time requirement,has many problems such as highly correlated initial values of the expression parameters,the need to pre-estimate the trend term shape,and poor fitting accuracy at low signal-to-noise ratios.In order to achieve real-time and robust trend term removal,a new trend term removal method using genetic programming(GP)in symbolic regression is constructed in this paper,and the FTIR simulation interference results and experimental measurement data for common volatile organic compounds(VOCs)gases are analyzed.The results show that the genetic programming algorithm can both reduce the initial value requirement and greatly improve the trend term accuracy by 20%-30% in three evaluation indicators,which is suitable for gas FTIR detection in complex scenarios.

基于DFT的旋转变压器信号偏差矫正方法研究

解码芯片在对旋转变压器输出的位置信号做处理的过程中,芯片在采样时容易产生各种非理想偏差,这会造成转子位置估算精度的急剧下降。针对该问题,分析了电压信号中的幅值偏差和正交偏差会对旋转变压器解码的输出角度叠加一个2倍频的波动,直流偏差会叠加一个同频波动的问题,提出了一种基于离散傅里叶变换(DFT)的输入矫正法用于实现旋转变压器输出信号的偏差矫正,同时有效降低一次二次波动。该方法首先离散采样信号,通过DFT公式提取旋转变压器输出信号的直流信号和基频信号;然后基于直流信号和基频信号先后计算直流偏差、幅值偏差和正交偏差,通过控制器实现偏差值矫正。最后,仿真和试验结果表明,在芯片采样产生偏差时,所提出的偏差提取方法有效,试验中相应的正余弦输出信号指定阶次的波动更小。

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transformation kernel. The EFFT＇s additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

基于STFT-ECA-ResNet18网络模型的滚动轴承变负载故障诊断

针对传统方法处理变负载轴承故障诊断时存在的自适应能力弱,模型泛化性差的问题,提出了一种改进的基于深度残差网络的故障诊断方法。首先,将采集到的一维时间序列信号进行短时傅里叶变换得到二维时频数据,再利用二维卷积神经网络从变换后的数据中提取特征。然后,通过高效通道注意力机制获取通道全局信息并对其权值进行调整,以增强改进网络模型的泛化能力,使其在变负载工况下分类效果得到提高。最后,通过仿真对所提方法进行了验证,结果表明相比传统方法诊断效果改进明显。

基于FrFT-Keystone运动补偿的OFDM声纳高速微弱目标相参积累检测算法

针对水下目标探测中使用的正交频分复用信号,提出了一种针对高速微弱目标的相参积累算法,以解决多脉冲积累下由目标机动引起的较大相位变化和由水下环境中信噪比低导致的相参积累增益不足的问题。所提算法利用分数阶傅里叶变换来估计目标的运动参数并进行补偿,并结合Keystone变换,实现对高速微弱目标的多脉冲相参积累。理论推导和仿真实验结果表明,所提算法能够有效补偿高速目标脉冲间的相位移动,并在低信噪比环境下取得较好的能量积累效果。

基于MDCFT与水平集的高海情弹载雷达成像检测方法

针对舰船三维摆动和海尖峰制约高海情环境弹载雷达探测性能的问题,面向高海情探测环境提出了一种新的成像检测思路。首先,基于高海情环境分别建立舰船与海杂波回波模型;其次,将改进离散调频傅里叶变换算法(modified discrete chirp Fourier transform, MDCFT)引入回波多普勒成像,消除了高阶项相位导致的散焦现象;在此基础上,利用水平集算法分割目标与背景区域,然后利用聚类算法确定每个目标区域;最后,基于提取的目标特征判决每个区域对应的目标身份。利用仿真数据的实验结果验证了所提算法的有效性。所提方法综合考虑了成像与检测环节性能的提升,为高海情环境下的弹载雷达制导提供了一种可行思路。

Fractional Fourier Transformation for Quantum Mechanical Wave Functions Studied by Virtue of IWOP Technique

Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.

基于移动平台的便携式FTIR灾害现场气体检测技术

傅里叶红外光谱技术(FTIR)的引入极大地提升了气体的检测速度和准确性。然而在石油化工泄露和爆炸、森林火灾等突发危险现场,存在着人力无法现场检测的情况。为了应对这种场景,开发了基于移动平台的便携式FTIR灾害现场气体检测方法。通过将云服务器和树莓派的优势相结合实现远程操作移动平台,将搭载便携式FTIR光谱仪的移动平台远程操作驶入现场,并及时通过4G/5G模块传回现场位置数据、视频数据和光谱气体浓度数据。最后,在野外基地利用该平台进行了实测,对CO_(2)、CO、SO_(2)、C_(6)H_(6)等多种污染气体进行了检测,结果验证了该系统在野外工况下的可靠性。本工作为FTIR光谱仪或其他光谱类检测系统在移动平台上的集成应用提供了思路和解决方案。

大点数FFT在“申威26010”上的并行优化

根据“神威·太湖之光”超级计算机所用国产“申威26010”处理器的架构特点和编程规范,提出针对大点数FFT的众核并行优化方案.该方案源自经典的Cooley-Tukey FFT算法,通过将一维大点数数据迭代分解为二维小规模矩阵进行并行加速.为了解决矩阵“列FFT”的读写、转置和计算问题,提出“列均分-行连续”的读写策略,通过对数据进行合理的分配、重排、交换,结合SIMD向量化、旋转因子优化、双缓冲、寄存器通信、跨步传输等优化手段,充分利用了众核处理器的计算资源和传输带宽.实验结果显示,单核组64从核并行程序较主核运行FFTW库,可以达到最高65x、平均48x以上的加速比.

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.