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.

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.

Cardiac arrhythmias detection in an ECG beat signal using fast fourier transform and artificial neural network

Cardiac Arrhythmias shows a condition of abnor-mal electrical activity in the heart which is a threat to humans. This paper presents a method to analyze electrocardiogram (ECG) signal, extract the fea-tures, for the classification of heart beats according to different arrhythmias. Data were obtained from 40 records of the MIT-BIH arrhythmia database (only one lead). Cardiac arrhythmias which are found are Tachycardia, Bradycardia, Supraventricular Tachycardia, Incomplete Bundle Branch Block, Bundle Branch Block, Ventricular Tachycardia. A learning dataset for the neural network was obtained from a twenty records set which were manually classified using MIT-BIH Arrhythmia Database Directory and docu- mentation, taking advantage of the professional experience of a cardiologist. Fast Fourier transforms are used to identify the peaks in the ECG signal and then Neural Networks are applied to identify the diseases. Levenberg Marquardt Back-Propagation algorithm is used to train the network. The results obtained have better efficiency then the previously proposed methods.

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.

Comparison of computation time for estimation of dominant frequency of atrial electrograms: Fast fourier transform, blackman tukey, autoregressive and multiple signal classification

Dominant frequency (DF) of electrophysiological data is an effective approach to estimate the activation rate during Atrial Fibrillation (AF) and it is important to understand the pathophysiology of AF and to help select candidate sites for ablation. Frequency analysis is used to find and track DF. It is important to minimize the catheter insertion time in the atria as it contributes to the risk for the patients during this procedure, so DF estimation needs to be obtained as quickly as possible. A comparison of computation tim- es taken for spectrum estimation analysis is presented in this paper. Fast Fourier Transform (FFT), Blackman-Tukey (BT), Autoregressive (AR) and Multiple Signal Classification (MUSIC) methods are used to obtain the frequency spectrum of the signals. The time to produce DF was measured for each method. The method which takes the shortest time for analysis is selected for real time application purpose.

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.

Fast Fourier Transform of Multi-Assets Options under Economic Recession Induced Uncertainties

A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asset Options under Economic Recession Induced Uncertainties. The issue of multi-dimension in both finite and infinite case of Options is part of the focus of this research. The notion of economic recession was incorporated. An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free. Nigeria economic recession outbreak in 2016 and its effects on the uncertainty of the payoffs of Nigeria Stocks Exchange (NSE) among other investments was among the motivating factors for proposing economic recession induced volatility in options pricing. The application of the proposed Fast Fourier Transform algorithm in handling multi-assets options was shown. A new result on options pricing was achieved and capable of yielding efficient option prices during and out of recession. Numerical results were presented on assets in 3-dimensions as an illustration taking Black Scholes prices as a bench mark for method effectiveness comparison. The key findings of this research paper among other crucial contributions could be seen in computational procedure of options valuation in multi-dimensions and uncertainties in options payoffs under the exposure of economic recession.

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 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.

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.

Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform

The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modulus of double discrete Fourier transform dependent on two parameters, are constructed and justified.

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.

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.

羽毛球极限挥拍速度与Fourier级数展开

为帮助羽毛球爱好者迅速提高挥拍技巧以及有效分析专业运动员的极限挥拍速度,基于实数域和复数域的傅里叶级数展开以及FFT(快速傅里叶变换)算法建立了理论向量模型。通过高阶求导计算,得到了羽毛球的理论极限挥拍速度。同时从理论上证明一般结论:击球速度在各关节运动方向一致时达到极大值,一般阶梯函数展开的极值点存在,且在斜率极大值处唯一取得。从而揭示了傅里叶级数在实数域和复数域之间的部分联系。此外,利用OpenPose人体姿态识别技术分析视频,建立实际向量模型,计算了羽毛球爱好者和专业运动员的实际速度,并将其与理论极限速度进行了对比,得出专业运动员相比羽毛球爱好者更贴近理论极限模型的结论。通过该结论验证此前理论模型的正确性,若羽毛球爱好者的挥拍动作更贴合理论极限模型,则更能达到极限速度,进而提升球技。

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.

星载SAR在轨成像高效处理系统硬件实现设计

星载合成孔径雷达(Synthetic Aperture Radar,SAR)在轨成像技术是灾害检测、军事侦察等高时效遥感应用场景的关键手段,以现场可编程门阵列(Field-Programmable Gate Array,FPGA)+数字信号处理器(Digital Signal Processing/Processor,DSP)为处理核心是一种搭建星载SAR在轨成像系统的典型方案,在异构算力、能效比、灵活度等方面综合评价良好。但现有的FPGA+DSP系统在算法支持、大粒度处理、片上并行加速、复杂矩阵转置方面仍研究不足,成像性能仍然有较大提升空间。本文对支持大斜视、高分辨成像的非线性调频变标算法(Nonlinear Chirp Scaling Algorithm,NCS)算法进行分析,根据运算复杂度和类型将算法划分为主流程和辅助路程,以此为依据提出NCS算法在FPGA+DSP系统中的异构映射方案;针对多通道快速傅里叶变换(Fast Fourier Transform,FFT)处理后数据存储形式发生变换、难以流水处理的问题,提出基于时频抽取切换的多通道FFT协同处理方法,保证多通道FFT处理高效进行;针对不同粒度、不同并行度场景下转置需求复杂多变的问题,提出基于X-直接存储器访问(X-Direct Memory Access,XDMA)+片上分割转置的通用交叉转置方案。本文采用2片VX690T FPGA和2片FT6678 DSP为核心处理器研制了星载SAR成像板卡,实现了提出的系统设计方案。同时,本文搭建了基于模拟源+地检的验证环境,对条带/扫描/聚束/滑聚/TOPS模式的仿真点阵数据和条带/滑聚模式的实测数据进行处理。点阵数据的二维峰值旁瓣比约为-13.2 dB,二维积分旁瓣比约为-10.1 dB,成像质量良好;以条带模式为例,图像尺寸为32K×16K,基于NCS算法的平均成像时间为7.81 s,成像速度较现有方案大幅提升。

基于STM32的辨音识别系统的设计与应用

声音识别技术能够用于多种环境参数检测,本文采用STM32的DSP技术,对全向拾音器采集到环境声音进行快速傅里叶变换(FFT),获取待测声音的主频率和次频率,通过液晶屏显示采集信号的强度和主要频率分量。该设备能够有效对环境声音的主要参赛进行检测,在噪声检测和一般设备运行故障检测具有较高的适用性。

卡斯卡迪亚慢滑移信息的GNSS时空探测

针对断层慢滑移时空分布信息探测困难的问题,基于全球卫星导航系统(GNSS)坐标序列,提出一种利用多通道奇异谱分析(MSSA)探测卡斯卡迪亚消减带慢滑移事件时空分布的方法:根据慢滑移分量的振荡特点确定窗口长度,采用时间迟滞矩阵对协方差阵进行增广,以提高对异常信息的识别能力;对振幅归一化获取空间响应,通过快速傅里叶变换分析慢滑移频谱特征。结果表明,卡斯卡迪亚消减带2007-01-05—2007-02-23和2008-04-22—2008-06-14发生了2次慢滑移事件,2次事件呈东南、西北区域的反向运动特征,且东南部响应程度明显高于西北地区;频谱特征显示,慢滑移信息表现为低频特征,且主要为随机游走噪声。研究结果可为板内地震前兆性信息探测提供参考。