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.

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.

Adaptive Short-Time Fractional Fourier Transform Based on Minimum Information Entropy

Traditional short-time fractional Fourier transform(STFrFT)has a single and fixed window function,which can not be adjusted adaptively according to the characteristics of fre-quency and frequency change rate.In order to overcome the shortcomings,the STFrFT method with adaptive window function is proposed.In this method,the window function of STFrFT is ad-aptively adjusted by establishing a library containing multiple window functions and taking the minimum information entropy as the criterion,so as to obtain a time-frequency distribution that better matches the desired signal.This method takes into account the time-frequency resolution characteristics of STFrFT and the excellent characteristics of adaptive adjustment to window func-tion,improves the time-frequency aggregation on the basis of eliminating cross term interference,and provides a new tool for improving the time-frequency analysis ability of complex modulated sig-nals.

Application of short-time Fourier transform to high-rise frame structural-health monitoring based on change of inherent frequency over time

The high-rise frame structure has become more and more widespread, like its damage from the complication of the environment. The traditional method of damage detection, which is only suitable for the stationary signal, does not apply to a high-rise frame structure because its damage signal is non-stationary. Thus, this paper presents an application of the short-time Fourier transform(STFT) to damage detection of high-rise frame structures. Compared with the fast Fourier transform, STFT is found to be able to express the frequency spectrum property of the time interval using the signal within this interval. Application of STFT to analyzing a Matlab model and the shaking table test with a twelve-story frame-structure model reveals that there is a positive correlation between the slope of the frequency versus time and the damage level. If the slope is equal to or greater than zero, the structure is not damaged. If the slope is smaller than zero, the structure is damaged, and the less the slope is, the more serious the damage is. The damage results from calculation based on the Matlab model are consistent with those from the shaking table test, demonstrating that STFT can be a reliable tool for the damage detection of high-rise frame structures.

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。

The Similarity Transformation of Regularizing Functionals and Simularity Property of Their Fourier Transformations

Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.

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.

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.

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.

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.

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.

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.

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.

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.

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.