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.

Fast GNSS Acquisition Algorithm Based on SFFT with High Noise Immunity

The Global Navigation Satellite System(GNSS)has been widely used in various fields.To achieve positioning,the receiver must first lock the satellite signal.This is a complicated and expensive process that consumes a lot of resources of the receiver.For this reason,this paper proposes a new fast acquisition algorithm with High Signal-tonoise ratio(SNR)performance based on sparse fast Fourier transform(HSFFT).The algorithm first replaces the IFFT process of the traditional parallel code phase capture algorithm with inverse sparse fast Fourier transform(ISFFT)with better computing performance,and then uses linear search combined with code phase discrimination to replace the positioning loop and the estimation loop with poor noise immunity in ISFFT.Theoretical analysis and simulation results show that,compared with the existing SFFT parallel code phase capture algorithm,the calculation amount of this algorithm is reduced by 19%,and the SNR performance is improved by about 5dB.Compared with the classic FFT parallel code phase capture algorithm,the calculation amount of the algorithm in this paper is reduced by 43%,and when the capture probability is greater than 95%,the SNR performance of the two is approximately the same.

Classification of Electroencephalogram Signals Using LSTM and SVM Based on Fast Walsh-Hadamard Transform

Classification of electroencephalogram(EEG)signals for humans can be achieved via artificial intelligence(AI)techniques.Especially,the EEG signals associated with seizure epilepsy can be detected to distinguish between epileptic and non-epileptic regions.From this perspective,an automated AI technique with a digital processing method can be used to improve these signals.This paper proposes two classifiers:long short-term memory(LSTM)and support vector machine(SVM)for the classification of seizure and non-seizure EEG signals.These classifiers are applied to a public dataset,namely the University of Bonn,which consists of 2 classes–seizure and non-seizure.In addition,a fast Walsh-Hadamard Transform(FWHT)technique is implemented to analyze the EEG signals within the recurrence space of the brain.Thus,Hadamard coefficients of the EEG signals are obtained via the FWHT.Moreover,the FWHT is contributed to generate an efficient derivation of seizure EEG recordings from non-seizure EEG recordings.Also,a k-fold cross-validation technique is applied to validate the performance of the proposed classifiers.The LSTM classifier provides the best performance,with a testing accuracy of 99.00%.The training and testing loss rates for the LSTM are 0.0029 and 0.0602,respectively,while the weighted average precision,recall,and F1-score for the LSTM are 99.00%.The results of the SVM classifier in terms of accuracy,sensitivity,and specificity reached 91%,93.52%,and 91.3%,respectively.The computational time consumed for the training of the LSTM and SVM is 2000 and 2500 s,respectively.The results show that the LSTM classifier provides better performance than SVM in the classification of EEG signals.Eventually,the proposed classifiers provide high classification accuracy compared to previously published classifiers.

Fast Digital Correlation Calculation Method in Extended Beacon Wavefront Detection

On the basis of Hartmann Shack sensor imaging analysis, a new method is presented with which the wavefront slope can be obtained when the object is incoherent and extended. This method, which is demonstrated by both theoretical interpreting and computer simulation, explains how to measure the wavefront slope difference between two sub apertures through the determination of image displacements on detector plane. It includes a fast and accurate digital algorithm for detecting wavefront disturbance, which is much suitable for realization in such electrical hardwares as digital signal processors.

Enhanced Steganalysis for Color Images Using Curvelet Features and Support Vector Machine

Algorithms for steganography are methods of hiding data transfers in media files.Several machine learning architectures have been presented recently to improve stego image identification performance by using spatial information,and these methods have made it feasible to handle a wide range of problems associated with image analysis.Images with little information or low payload are used by information embedding methods,but the goal of all contemporary research is to employ high-payload images for classification.To address the need for both low-and high-payload images,this work provides a machine-learning approach to steganography image classification that uses Curvelet transformation to efficiently extract characteristics from both type of images.Support Vector Machine(SVM),a commonplace classification technique,has been employed to determine whether the image is a stego or cover.The Wavelet Obtained Weights(WOW),Spatial Universal Wavelet Relative Distortion(S-UNIWARD),Highly Undetectable Steganography(HUGO),and Minimizing the Power of Optimal Detector(MiPOD)steganography techniques are used in a variety of experimental scenarios to evaluate the performance of the proposedmethod.Using WOW at several payloads,the proposed approach proves its classification accuracy of 98.60%.It exhibits its superiority over SOTA methods.

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.

基于图控分离和2次分类的无人机信号识别方法

无人机(unmanned aerial vehicle, UAV)行业的快速发展给重要场所的低空空域带来安全隐患.为了对无人机实施有效管制,研制一套能够识别无人机信号的无线电侦测系统有重要意义.针对相似无人机之间识别困难的问题,提出了一种基于图控分离和2次分类的无人机信号识别方法.该方法基于无人机图像传输信号(image transmission signal, ITS)的循环特性提取其时域参数,采用分类决策树对无人机进行初步分类识别;再通过分离无人机的图像传输信号与飞行控制信号(flight control signal, FCS)的方式分别提取其时频特征参数;最后进行了2次分类识别.实验结果表明,对于6种常见无人机的通信信号,在信噪比(signal-to-noise ratio, SNR)为0 d B时平均识别准确率可达97.4%,说明该方法可以精确识别无人机.

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.

Quantifying Kinematic Tremor in an NGLY1-Deficient Individual: A Case Study

NGLY1 Deficiency is an autosomal recessive congenital disorder that has been identified in less than 100 individuals. Most individuals with NGLY1 Deficiency display hyperkinetic movement disorders, including choreiform, athetoid, dystonic myoclonic, dyskinetic, and dysmetric movements. Developing a consistent and concise consensus on the classification and evaluation of tremors is essential to forward the research and treatment of tremors. It has also been reported that some individuals with NGLY1 Deficiency demonstrate tremor, but such tremor has never been formally investigated. The primary objective of this study is to determine if an individual with NGLY1 Deficiency demonstrates an identifiable tremor during a series of arm movements and, if so, describe the frequency and power characteristics of that tremor. Arm movement kinematics were obtained using a 16-camera Vicon system, and time series trajectory waveforms for three planes of a marker placed on the hand were developed. Custom MATLAB scripts were utilized to compute Fast Fourier Transformations of the data within the identified waveform segments. A mean frequency of 2.30 Hz (SD = 1.05) with a mean power of 5.02 |P1(f)| (SD = 4.63) suggests that our participant’s kinematic data did display a persistent tremor in both hands across all tasks and movement planes. Analyses of the reaching hand and the non-reaching hand suggest the participant displayed an action tremor in both postural and intention (kinetic) tremors. Future directions should include assessing additional individuals with NGLY1 Deficiency to determine if the tremor is a distinguishable disorder behavior. Additionally, evaluating other anatomical sites, such as the elbow, head, and lower limbs, would provide further insights into the characteristics of this tremor.

Enhanced Wideband Frequency Estimation via FFT: Leveraging Polynomial Interpolation and Array Indexing

Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.

FAST IMPLEMENTATION OF CONVOLUTION BACKPROJECTION ALGORITHM IN SPOTLIGHT SAR

A fast implementation of the convolution backprojection（CBP）algorithm in spotlight synthetic aperture radar（SAR）is presented based on the fast Fourier transform（FFT）.Traditionally,the computation of the ＇backprojection＇ process is expensive,since resampling in the process is implemented by using the interpolation operation.By analyzing the relative location relationship among different pixels,the algorithm realizes the ＇backprojection＇ using a series of FFTs instead of the interpolation operation.The point target simulation validates that the new algorithm accelerates the CBP algorithm,and the computational rate increases about 85%.

Ultrafast multi-target control of tightly focused light fields

The control of ultrafast optical field is of great interest in developing ultrafast optics as well as the investigation on vari-ous light-matter interactions with ultrashort pulses.However,conventional spatial encoding approaches have only lim-ited steerable targets usually neglecting the temporal effect,thus hindering their broad applications.Here we present a new concept for realizing ultrafast modulation of multi-target focal fields based on the facile combination of time-depend-ent vectorial diffraction theory with fast Fourier transform.This is achieved by focusing femtosecond pulsed light carrying vectorial-vortex by a single objective lens under tight focusing condition.It is uncovered that the ultrafast temporal de-gree of freedom within a configurable temporal duration(~400 fs)plays a pivotal role in determining the rich and exotic features of the focused optical field at one time,namely,bright-dark alternation,periodic rotation,and longitudinal/trans-verse polarization conversion.The underlying control mechanisms have been unveiled.Besides being of academic in-terest in diverse ultrafast spectral regimes,these peculiar behaviors of the space-time evolutionary beams may underpin prolific ultrafast-related applications such as multifunctional integrated optical chip,high-efficiency laser trapping,micro-structure rotation,super-resolution optical microscopy,precise optical measurement,and liveness tracking.

Fast Computation of Cross-Ambiguity Function

A novel method based on zoom fast Fourier transform（FFT） is proposed for minimizing the burden processing of cross-ambiguity functions without affecting performance. The low-pass anti-aliasing filter in zoom FFT is realized by using the multistage filtering technique and the weighting processing is employed in the first stage filter to get rid of the redundancy of the computation. In practical systems, the input data is divided into overlapped data frames to avoid loss of detection ability which results in the rapid increase of computational complexity. A segment technique is also proposed in which CAF calculation of overlapped data frames is viewed as slide window FFT to decrease the computational complexity. The experimental results show that compared to the conventional methods, the proposed method can lower computational complexity and is consistent with the real time implementation in existing high-speed digital processors.

A fast acquisition method of DSSS signals using differential decoding and fast Fourier transform

In low earth orbit (LEO) satellite or missile communication scenarios, signals may experience extremely large Doppler shifts and have short visual time. Thus, direct sequence spread spectrum (DSSS) systems should be able to achieve acquisition in a very short time in spite of large Doppler frequencies. However, the traditional methods cannot solve it well. This work describes a new method that uses a differential decoding technique for Doppler mitigation and a batch process of FFT (fast Fourier transform) and IFFT (invert FFT) for the purpose of parallel code phase search by frequency domain correlation. After the code phase is estimated, another FFT process is carried out to search the Doppler frequency. Since both code phase and Doppler frequency domains are searched in parallel, this architecture can provide acquisition fifty times faster than conventional FFT methods. The performance in terms of the probability of detection and false alarm are also analyzed and simulated, showing that a signal-to-noise ratio (SNR) loss of 3 dB is introduced by the differential decoding. The proposed method is an efficient way to shorten the acquisition time with slightly hardware increasing.

A high performance fast-Fourier-transform spectrum analyzer for measuring spin noise spectrums

A high performance fast-Fourier-transform (FFT) spectrum analyzer, which is developed for measure spin noise spectrums, is presented in this paper. The analyzer is implemented with a field-programmable-gate-arrays (FPGA) chip for data and command management. An analog-to-digital-convertor chip is integrated for analog signal acquisition. In order to meet the various requirements of measuring different types of spin noise spectrums, multiple operating modes are designed and realized using the reprogrammable FPGA logic resources. The FFT function is fully managed by the programmable resource inside the FPGA chip. A 1 GSa/s sampling rate and a 100 percent data coverage ratio with non-dead-time are obtained. 30534 FFT spectrums can be acquired per second, and the spectrums can be on-board accumulated and averaged. Digital filters, multi-stage reconfigurable data reconstruction modules, and frequency down conversion modules are also implemented in the FPGA to provide flexible real-time data processing capacity, thus the noise floor and signals aliasing can be suppressed effectively. An efficiency comparison between the FPGA-based FFT spectrum analyzer and the software-based FFT is demonstrated, and the high performance FFT spectrum analyzer has a significant advantage in obtaining high resolution spin noise spectrums with enhanced efficiency.

A sapphire fibre thermal probe based on fast Fourier transform and phase-lock loop

A sapphire fibre thermal probe with Cr^3＋ ion-doped end is developed by using the laser heated pedestal growth method. The fluorescence thermal probe offers advantages of compact structure, high performance and ability to withstand high temperature in a detection range from room temperature to 450℃. Based on the fast Fourier transform （FFT）, the fluorescence lifetime is obtained from the tangent function of phase angle of the non-zeroth terms in the FFT result. This method has advantages such as quick calculation, high accuracy and immunity to the background noise. This FFT method is compared with other traditional fitting methods, indicating that the standard deviation of the FFT method is about half of that of the Prony method and about 1/6 of that of the log-fit method. And the FFT method is immune to the background noise involved in a signal. So, the FFT method is an excellent way of processing signals. In addition, a phase-lock amplifier can effectively suppress the noise.

Combining Cubic Spline Interpolation and Fast Fourier Transform to Extend Measuring Range of Reflectometry

The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.

Fast Fourier Transform Approximation of Foreign Currency Option Pricing Based on Exponential Lévy Model

To study the approximation of foreign currency option prices when the underlying assets＇ price dynamics are described by exponential Lévy processes, the convolution representations for option pricing formulas were given, and then the fast Fourier transform （FFT） algorithm was used to get the approximate values of option prices. Finally, a numerical example was given to demonstrate the calculate steps to the option price by FFT.

Medical Image Compression Using Wrapping Based Fast Discrete Curvelet Transform and Arithmetic Coding

Due to the development of CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography), EBCT (Electron Beam Computed Tomography), SMRI (Stereotactic Magnetic Resonance Imaging), etc. has enhanced the distinguishing rate and scanning rate of the imaging equipments. The diagnosis and the process of getting useful information from the image are got by processing the medical images using the wavelet technique. Wavelet transform has increased the compression rate. Increasing the compression performance by minimizing the amount of image data in the medical images is a critical task. Crucial medical information like diagnosing diseases and their treatments is obtained by modern radiology techniques. Medical Imaging (MI) process is used to acquire that information. For lossy and lossless image compression, several techniques were developed. Image edges have limitations in capturing them if we make use of the extension of 1-D wavelet transform. This is because wavelet transform cannot effectively transform straight line discontinuities, as well geographic lines in natural images cannot be reconstructed in a proper manner if 1-D transform is used. Differently oriented image textures are coded well using Curvelet Transform. The Curvelet Transform is suitable for compressing medical images, which has more curvy portions. This paper describes a method for compression of various medical images using Fast Discrete Curvelet Transform based on wrapping technique. After transformation, the coefficients are quantized using vector quantization and coded using arithmetic encoding technique. The proposed method is tested on various medical images and the result demonstrates significant improvement in performance parameters like Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).

FAST FOURIER TRANSFORMS ON BINARY FIELDS

We give a unified treatment of Fast Fourier Transforms for UDMD systems which contains, as special cases, Fast Fourier algorithms for character groups of many subgroups associated with binary fields.