Experimental Consideration of Two-Dimensional Fourier Transform Spectroscopy

Two-dimensional Fourier transform(2D FT) spectroscopy is an important technology that developed in recent decades and has many advantages over other ultrafast spectroscopy methods. Although 2D FT spectroscopy provides great opportunities for studying various complex systems, the experimental implementation and theoretical description of 2D FT spectroscopy measurement still face many challenges, which limits their wide application.Recently, the 2D FT spectroscopy reaches maturity due to many new developments which greatly reduces the technical barrier in the experimental implementation of the 2D FT spectrometer. There have been several different approaches developed for the optical design of the 2D FT spectrometer, each with its own advantages and limitations. Thus, a procedure to help an experimentalist to build a 2D FT spectroscopy experimental apparatus is needed.This tutorial review is intending to provide an accessible introduction for a beginner to build a 2D FT spectrometer.

A Deepfake Detection Algorithm Based on Fourier Transform of Biological Signal

Deepfake-generated fake faces,commonly utilized in identity-related activities such as political propaganda,celebrity impersonations,evidence forgery,and familiar fraud,pose new societal threats.Although current deepfake generators strive for high realism in visual effects,they do not replicate biometric signals indicative of cardiac activity.Addressing this gap,many researchers have developed detection methods focusing on biometric characteristics.These methods utilize classification networks to analyze both temporal and spectral domain features of the remote photoplethysmography(rPPG)signal,resulting in high detection accuracy.However,in the spectral analysis,existing approaches often only consider the power spectral density and neglect the amplitude spectrum—both crucial for assessing cardiac activity.We introduce a novel method that extracts rPPG signals from multiple regions of interest through remote photoplethysmography and processes them using Fast Fourier Transform(FFT).The resultant time-frequency domain signal samples are organized into matrices to create Matrix Visualization Heatmaps(MVHM),which are then utilized to train an image classification network.Additionally,we explored various combinations of time-frequency domain representations of rPPG signals and the impact of attention mechanisms.Our experimental results show that our algorithm achieves a remarkable detection accuracy of 99.22%in identifying fake videos,significantly outperforming mainstream algorithms and demonstrating the effectiveness of Fourier Transform and attention mechanisms in detecting fake faces.

Security-Enhanced Directional Modulation Based on Two-Dimensional M-WFRFT

Directional modulation(DM)is one of the most promising secure communication techniques.However,when the eavesdropper is co-located with the legitimate receiver,the conventional DM has the disadvantages of weak anti-scanning capability,anti-deciphering capability,and low secrecy rate.In response to these problems,we propose a twodimensional multi-term weighted fractional Fourier transform aided DM scheme,in which the legitimate receiver and the transmitter use different transform terms and transform orders to encrypt and decrypt the confidential information.In order to further lower the probability of being deciphered by an eavesdropper,we use the subblock partition method to convert the one-dimensional modulated signal vector into a twodimensional signal matrix,increasing the confusion of the useful information.Numerical results demonstrate that the proposed DM scheme not only provides stronger anti-deciphering and anti-scanning capabilities but also improves the secrecy rate performance of the system.

A Physical Security Technology Based upon Doubly Multiple Parameters Weighted Fractional Fourier Transform

Enhancing the security of the wireless communication is necessary to guarantee the reliable of the data transmission, due to the broadcast nature of wireless channels. In this paper, we provide a novel technology referred to as doubly multiple parameters weighted fractional Fourier transform(DMWFRFT), which can strengthen the physical layer security of wireless communication. This paper introduces the concept of DM-WFRFT based on multiple parameters WFRFT(MP-WFRFT), and then presents its four properties. Based on these properties, the parameters decryption probability is analyzed in terms of the number of parameters. The number of parameters for DM-WFRFT is more than that of the MP-WFRFT,which indicates that the proposed scheme can further strengthen the the physical layer security. Lastly, some numerical simulations are carried out to illustrate that the efficiency of proposed DM-WFRFT is related to preventing eavesdropping, and the effect of parameters variety on the system performance is associated with the bit error ratio(BER).

Mid-infrared Optical Frequency Comb-based Fourier Transform Spectrometer for Broadband Molecular Spectroscopy

Optical frequency combbased Fourier transform spectroscopy has the features of broad spectral bandwidth,high sensitivity,andmultiplexed trace gas detection,which has valuable application potential in the fields of precision spectroscopy and trace gas detection.Here,we report the development of a mid-infrared Fourier transform spectrometer based on an optical frequency comb combined with a Herriott-type multipass cell.Using this instrument,the broadband absorption spectra of several important molecules,including methane,acetylene,water molecules and nitrous oxide,are measured by near real-time data acquisition in the 2800-3500 cm^(-1)spectral region.The achieved minimum detectable absorption of the instrument is 4.4×10^(-8)cm^(-1)·Hz^(-1/2)per spectral element.Broadband spectra of H_(2)0 are fited using the Voigt profile multispectral fitting technique and the consistency of the concentration inversion is 1%.Our system also enables precise spectroscopic measurements,and it allows the determination of the spectral line positions and upper state constants of N_(2)O in the(0002)-(1000)band,with results in good agreement with those reported by Toth[Appl.Opt.30,5289(1991)].

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.

Design and implementation of code acquisition using sparse Fourier transform

Code acquisition is the kernel operation for signal synchronization in the spread-spectrum receiver.To reduce the computational complexity and latency of code acquisition,this paper proposes an efficient scheme employing sparse Fourier transform(SFT)and the relevant hardware architecture for field programmable gate array(FPGA)and application-specific integrated circuit(ASIC)implementation.Efforts are made at both the algorithmic level and the implementation level to enable merged searching of code phase and Doppler frequency without incurring massive hardware expenditure.Compared with the existing code acquisition approaches,it is shown from theoretical analysis and experimental results that the proposed design can shorten processing latency and reduce hardware complexity without degrading the acquisition probability.

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.

Theory and algorithms for two-dimensional warped discrete Fourier transform

In this paper, the two-dimensional Warped Discrete Fourier Transform （2-D WDFT） is developed based on the concept of the 1-D WDFT. An exact computation algorithm is developed for 2-D WDFT based on matrix factorizing with special structure. A fast algorithm is then proposed to reduce greatly the computational complexity of the inverse 2-D WDFT. Finally, numerical examples are given to show the efficiency of the proposed approach.

基于时频图与视觉Transformer的滚动轴承智能故障诊断方法

基于循环神经网络的故障诊断方法在计算过程中难以保存间隔时间过长的信息且无法并行计算,在大型数据建模方面存在不足,为提高轴承故障诊断工作的效率及准确性,提出了一种基于短时傅里叶变换时频图与视觉Transformer(ViT)的轴承故障诊断方法:通过短时傅里叶变换将原始振动信号转换为二维时频图像,再将时频图作为特征图输入ViT网络中进行训练,详细分析网络参数对故障诊断性能和计算复杂度的影响,构建最优模型结构,最终实现轴承的故障诊断。采用凯斯西储大学和江南大学轴承数据对模型进行验证,结果表明该模型可以有效结合短时傅里叶变换在处理时变信号方面的优势和ViT网络强大的图像分类能力,具有更高的诊断精度和更好的泛化性、通用性。

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.

Two-dimensional nanomaterials confined single atoms: New opportunities for environmental remediation

Two-dimensional(2D)supports confined single-atom catalysts(2D SACs)with unique geometric and electronic structures have been attractive candidates in different catalytic applications,such as energy conversion and storage,value-added chemical synthesis and environmental remediation.However,their environmental appli-cations lack of a comprehensive summary and in-depth discussion.In this review,recent progresses in synthesis routes and advanced characterization techniques for 2D SACs are introduced,and a comprehensive discussion on their applications in environmental remediation is presented.Generally,2D SACs can be effective in catalytic elimination of aqueous and gaseous pollutants via radical or non-radical routes and transformation of toxic pollutants into less poisonous species or highly value-added products,opening a new horizon for the contami-nant treatment.In addition,in-depth reaction mechanisms and potential pathways are systematically discussed,and the relationship between the structure-performance is highlighted.Finally,several critical challenges within this field are presented,and possible directions for further explorations of 2D SACs in environmental remediation are suggested.Although the research of 2D SACs in the environmental application is still in its infancy,this review will provide a timely summary on the emerging field,and would stimulate tremendous interest for designing more attractive 2D SACs and promoting their wide applications.

Two-dimensional plane strain consolidation of unsaturated soils considering the depth-dependent stress

In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.

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.

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.

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的频率敏感双分支Transformer多变量长时间序列预测方法

在进行多变量长时间序列预测时,仅利用时域分析通常无法充分捕捉长时间序列依赖,而这会导致信息利用率不足、预测精度不够高。因此,结合频域时域分析,提出一种基于离散傅里叶变换(DFT)的频率敏感双分支多变量长时间序列预测(FSDformer)方法。首先,通过DFT实现时间和频率的相互转换,从而将复杂的时间序列数据分解为结构简单的低频趋势项、中频季节项和高频余项3个分量;其次,采用双分支结构,针对中高频分量预测,应用Encoder-Decoder结构,设计了周期性增强注意力机制;针对低频趋势分量预测,采用多层感知机(MLP)结构;最后将中高频分量与低频分量预测结果相加,得到多变量长时间序列的最终预测结果。在2个数据集上把FSDformer与其他5个经典算法进行了对比分析,在Electricity数据集上,当历史序列长度为96,预测序列长度为336时,相较于Autoformer等对比算法,FSDformer的平均绝对误差(MAE)下降了11.5%~29.1%,均方误差(MSE)下降了20.9%~43.7%,达到了最优预测精度。实验结果表明,FSDformer能有效捕捉长时间序列的相关依赖,在提升预测精度和计算效率的同时,增强了模型预测的稳定性。

基于Fourier变换红外光谱分析咖啡豆成分

采用Fourier变换红外光谱对不同产区、不同海拔的5组浅中烘焙的咖啡豆样品进行分析,根据官能团的红外光谱特征峰分析样品主要成分;为进一步分析5组样品的成分差异,对原始光谱进行二阶导数处理,结合聚类分析理论建立平均偏离分析方法,计算出5组样品间的平均偏离大小并进行分析.结果表明:5组样品的红外光谱特征峰峰形相似,即主要成分相同;根据红外光谱得到平均偏离大小与产区海拔差值呈正相关.研究结果为分析咖啡豆产区和海拔提供鉴别依据,并对红外光谱研究提供一定参考.

分数阶Fourier变换的测不准原理

该文参考Fourier变换的性质研究了离散分数阶Fourier变换的测不准原理以及连续分数阶Fourier变换在Lebesgue测度下的测不准原理,使得分数阶Fourier变换的测不准原理性质更一般化.