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.

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.

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.

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.

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.

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 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.

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.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.

An Accurate Numerical Solution for the Modified Equal Width Wave Equation Using the Fourier Pseudo-Spectral Method

In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L2 and L∞ error norms are computed to study the accuracy and the simplicity of the presented method.

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.

Novel Lossless Compression Method Based on the Fourier Transform to Approximate the Kolmogorov Complexity of Elementary Cellular Automata

We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are widely used in image compression but their lossy nature exclude them as viable candidates for Kolmogorov Complexity approximations. For the first time, we present a way to adapt fourier transforms for lossless image compression. The proposed method has a very strong Pearsons correlation to existing complexity metrics and we further establish its consistency as a complexity metric by confirming its measurements never exceed the complexity of nothingness and randomness (representing the lower and upper limits of complexity). Surprisingly, many of the other methods tested fail this simple sanity check. A final symmetry-based test also demonstrates our method’s superiority over existing lossless compression metrics. All complexity metrics tested, as well as the code used to generate and augment the original dataset, can be found in our github repository: ECA complexity metrics1.

Visualization for Explanation of Deep Learning-Based Fault Diagnosis Model Using Class Activation Map

Permanent magnet synchronous motor(PMSM)is widely used in various production processes because of its high efficiency,fast reaction time,and high power density.With the continuous promotion of new energy vehicles,timely detection of PMSM faults can significantly reduce the accident rate of new energy vehicles,further enhance consumers’trust in their safety,and thus promote their popularity.Existing fault diagnosis methods based on deep learning can only distinguish different PMSM faults and cannot interpret and analyze them.Convolutional neural networks(CNN)show remarkable accuracy in image data analysis.However,due to the“black box”problem in deep learning models,the diagnostic results regarding providing accurate information to the user are uncertain.This paper proposes a motor fault diagnosis method based on improved deep residual network(ResNet)and gradient-weighted class activation mapping(Grad-CAM)to analyze demagnetization and eccentricity faults of permanent magnet synchronous motors,and the uncertainty limitation of fault diagnosis based on the convolutional neural network is overcome by the visual interpretation method.The improved ResNet is formed by using ResNet9 as the backbone network,replacing the last convolution layer with a atrous spatial pyramid pooling(ASPP),and adding a multi-scale feature fusion module and attention channel mechanism(CAM).The proposed model not only retains the effective extraction of image features by ResNet9 but also enhances the sensitivity field of the network through the hollow convolution pyramid and realizes the feature fusion of the web on different scales through the multi-scale feature fusion module(MSFFM),further improving the diagnostic accuracy of the network on different types of fault features.The diagnostic effect of the network is verified on the selfmade data set,which mainly includes five states:normal(He),25%demagnetization(De25),50%demagnetization(De50),10%static eccentricity(Se10),and 20%static eccentricity(Se20).The number of pictures in the training set is 6000,and the number in the test set is 1500.The average diagnostic accuracy of the improved ResNet on this dataset is 99.00%,which is 1.04%,8.89%,4.58%,and 7.22%higher than that of the multi-column convolutional neural network(MCNN),Bi-directional long short-term memory(Bi-LSTM),deep belief network(DBN),and recurrent neural network(RNN)models,respectively.Finally,gradient activation heat maps were used to globally average pool the final output feature map of the network to obtain feature weights.They were superimposed with the original image to get gradient activation heat maps of different grayscale images.The warmer the tone of the heat map,the greater the impact on the network diagnosis results,and then the demagnetization and eccentricity fault characteristics of the permanent magnet synchronous motor were determined-visual characterization of quantitative analysis.

A novel stochastic modeling framework for coal production and logistics through options pricing analysis

We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.

Spectral Analysis and Validation of Parietal Signals for Different Arm Movements

Brain signal analysis plays a significant role in attaining data related to motor activities.The parietal region of the brain plays a vital role in muscular movements.This approach aims to demonstrate a unique technique to identify an ideal region of the human brain that generates signals responsible for muscular movements;perform statistical analysis to provide an absolute characterization of the signal and validate the obtained results using a prototype arm.This can enhance the practical implementation of these frequency extractions for future neuro-prosthetic applications and the characterization of neurological diseases like Parkinson’s disease(PD).To play out this handling method,electroencepha-logram(EEG)signals are gained while the subject is performing different wrist and elbow movements.Then,the frontal brain signals and just the parietal signals are separated from the obtained EEG signal by utilizing a band pass filter.Then,feature extraction is carried out using Fast Fourier Transform(FFT).Subse-quently,the extraction process is done by Daubechies(db4)and Haar wavelet(db1)in MATLAB and classified using the Levenberg-Marquardt Algorithm.The results of the frequency changes that occurred during various wrist move-ments in the parietal region are compared with the frequency changes that occurred in frontal EEG signals.This proposed algorithm also uses the deep learn-ing pattern analysis network to evaluate the matching sequence for each action that takes place.Maximum accuracy of 97.2%and maximum error range of 0.6684%are achieved during the analysis.Results of this research confirm that the Levenberg-Marquardt algorithm,along with the newly developed deep learn-ing hybrid PatternNet,provides a more accurate range of frequency changes than any other classifier used in previous works of literature.Based on the analysis,the peak-to-peak value is used to define the threshold for the prototype arm,which performs all the intended degrees of freedom(DOF),verifying the results.These results would aid the specialists in their decision-making by facilitating the ana-lysis and interpretation of brain signals in the field of neuroscience,specifically in tremor analysis in PD.