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.

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.

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.

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.

Fast High Order Algorithm for Three-Dimensional Helmholtz Equation Involving Impedance Boundary Condition with Large Wave Numbers

Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.

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.

Phase Error Compensation of Three-Dimensional Reconstruction Combined with Hilbert Transform

Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method.A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light.According to the analysis of the influence of Gamma distortion on the phase calculation,the algorithm establishes the relationship model between phase error and harmonic coefficient,introduces phase shift to the signal,and keeps the signal amplitude constant while filtering out the DC component.The phase error is converted to the transform domain,and compared with the numeric value in the space domain.The algorithm is combined with a spiral phase function to optimize the Hilbert transform,so as to eliminate external noise,enhance the image quality,and get an accurate phase value.Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement.By performing phase error compensation for free-form surface objects,the phase error is reduced by about 26%,and about 27%of the image reconstruction time is saved,which further demonstrates the feasibility and effectiveness of the method.

Using three-dimensional discrete spherical Fourier descriptors based on surface curvature voxels for pollen particle recognition

This paper presents a new method for extract three-dimensional （3D） discrete spherical Fourier descriptors based on surface curvature voxels for pollen particle recognition. In order to reduce the high amount of pollen information and noise disturbance, the geometric normalized curvature voxels with the principal curvedness are first extracted to represent the intrinsic pollen volumetric data. Then the curvature voxels are decomposed into radial and angular components with spherical harmonic transform in spherical coordinates. Finally the 3D discrete Fourier transform is applied to the decomposed curvature voxels to obtain the 3D spherical Fourier descriptors for pollen recognition. Experimental results show that the presented descriptors are invariant to different pollen particle geometric transformations, such as pose change and spatial rotation, and can obtain high recognition accuracy and speed simultaneously.

基于频率Transformer-CNN耦合的烟雾分割模型研究

本文深入开展了输电线路附近山火实时监测过程中图像的烟雾分割方法研究,有助于对图像中烟雾体积、扩散方向和源头等准确提取信息,这对制定应急预案具有重要意义。为此,提出了一种名为CFTNet的双分支分割模型。该模型将频率Transformer分支与CNN分支结合起来,优化了全局和局部特征的表示。此外,本文还设计了一个混合自注意力融合模块(HSAM),以高效地融合来自频率Transformer分支和CNN分支的信息。研究表明,该算法的性能优于其他主流分割方法。

河渠附近潜水一维非稳定流模型Fourier快解求解

对垂向交换量影响下的河渠附近潜水一维非稳定流模型,采用Boussinesq方程的第一线性化方法,在利用Fourier变换求解时,随河渠水位f(t)的变化,需要复杂繁琐的积分变换过程。在f(t)不直接参与变换的前提下,将f(t)用运算符代替并运行于变换过程中,依据Fourier变换的微分性质和卷积定理等性质,建立这类模型普遍适用的含f(t)的理论通用解;依据理论通用解,给出f(t)为几个常用函数时的模型解析解;利用理论通用解的求解方法,可避免大部分繁杂的积分变换运算过程。针对不同的河渠水位变动与垂向补给组合条件,建立利用潜水位动态监测数据计算模型参数的拐点法和配线法;实例演示,模型参数的求算过程。

量化噪声对插值fast Fourier transform谐波估计的影响

插值fast Fourier transform(FFT)算法是对谐波频率、幅度和相位三参数进行精确估计的常见方法.信号中的噪声无疑会影响插值FFT算法的谐波估计结果.有文献讨论过信号中的白噪声对插值FFT算法谐波估计结果的影响,尚没有文献讨论过A/D(analog-to-digital)量化噪声对插值FFT算法谐波估计结果的影响.本文首先对插值FFT谐波估计算法做了简单介绍,接着对A/D量化噪声的特点进行了分析研究.在此基础上,仔细研究了量化噪声对插值FFT谐波估计方法的影响程度——给出了计算模型、进行了大量仿真计算、得出了量化噪声对谐波频率、幅度和相位3参数估计结果影响程度的结论.相信所得结论对电路设计中的A/D器件、信号调理器件等的选型有指导意义.

基于插值fast Fourier transform谐波分析的桥梁状态评估方法

桥梁的环境振动信号包含了各种环境噪声成分,如何从噪声影响中提取桥梁的真实自振频率,并进行桥梁状态评估是亟待解决的问题.本文对环境激励下的大跨桥梁响应信号进行了研究,根据环境激励在低频段近于平白噪声以及线性系统在环境激励下,各输出点测量信号之间相关函数与结构的脉冲响应函数具有相同的数学表达式——均是主频正弦函数的叠加这一特点,建立了插值fast Fourier transform(FFT)频谱校正技术分析各测点相关函数的方法.该方法能在白噪声背景下精确提取桥梁振动频率、幅度和相位等模态参数,简单实用,不仅能在线识别参数,而且对桥梁单点激励和多点同时激励均适用.将校正后的主频与三维有限元计算结果相对比,能对桥梁结构整体状态和工作性能进行评估.最后,一座实桥动力试验和计算结果证明了该方法的能有效用于运营条件下桥梁状态的评估.

NYFR output pulse radar signal TOA analysis using extended Fourier transform and its TOA estimation

Nyquist folding receiver (NYFR) is a typical wideband analog-to-information architecture. Focusing on the non-cooperative receiving, the pulse radar signal intercepted by the NYFR in time domain is analyzed. The NYFR outputs under different input conditions are investigated based on the extended Fourier transform (EFT) and the sampling theorem. Combining with the characteristic of the NYFR output in time domain, a new time of arrival (TOA) estimation method based on the energy envelope and the wavelet transform is proposed. The proposed estimation method can be adapted for the non-cooperative situation. It has no requirement for prior information to determine the threshold and is not necessary to transform the signal into baseband. Simulation results prove the correctness of the NYFR output expressions and show the efficacy of the proposed estimation method. © 2017 Beijing Institute of Aerospace Information.

Chirp-Rate Resolution of Fractional Fourier Transform in Multi-component LFM Signal

Distinguishing close chirp-rates of different linear frequency modulation （LFM） signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform （FrFT）. Then the expression of chirp-rate resolution in fractional Fourier domain （FrFD） was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can he omitted. What＇s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.

Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform

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.