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.

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.

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.

基于双窗全相位FFT的变流器阻抗高精度辨识新方法

为了提高变流器阻抗辨识精度,提出将布莱克曼双窗全相位快速傅里叶变换算法应用于并网变流器输出阻抗高精度辨识之中。首先,建立了dq坐标系下的三相并网变流器的dq阻抗模型;其次,基于原理分析论证了所提方法具有优良的频谱泄漏抑制性能以及较强的抗噪能力,特别适合于在施加小扰动信号背景下非线性特性较强的并网变流器输出阻抗的高精度辨识,并给出变流器阻抗辨识流程;最后,通过仿真试验,验证了方法的优越性。基于布莱克曼双窗全相位快速傅里叶变换的阻抗辨识方法,相比传统方法能以更高的精度辨识出变流器输出阻抗。

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 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.

Novel DDS Based OFDM Transmitter Structure without IFFT and Interpolation Filter

The traditional orthogonal frequency divi-sion multiplexing(OFDM)transmitter is implemented by inverse fast Fourier transform(IFFT),up-sampling and low pass shaping filter(LPSF),which occupy a large number of hardware resources and have long la-tency.To further meet the 5G and future 6G commu-nication requirements,this paper proposes a novel di-rect digital synthesis(DDS)based OFDM transmitter structure that can replace these modules.Due to the strong parallelism of the system structure,it is very suitable for implementation on field programable gate array(FPGA)platform.After making two special sim-plifications to the primary structure,the refined struc-ture becomes very simple compared with the tradi-tional structures.Most attractively,the proposed struc-ture has the following three advantages that i)the data transformation from frequency domain to time domain has zero latency,ii)the transformation length does not need to be an integer power of 2 and iii)the struc-ture does not even need to use any multiplier,thus leading to low implementation complexity and high speed.Comparative experiments are carried out on Intel FPGA platform which show that our DDS based structure can save more than half of the resources com-pared with the traditional structures and can provide the same bit error rate(BER)performance under the condition without using any LPSF.

Parameter Estimation of Sub-/Super-synchronous Oscillation Based on Interpolated All-phase Fast Fourier Transform with Optimized Window Function

In recent years,with increasing amounts of renewable energy sources connecting to power grids,sub-/super-synchronous oscillations(SSOs)occurred more frequently.Due to the time-variant nature of SsO magnitudes and frequencies,as well as the mutual interferences among SsO modes with close frequencies,the accurate parameter estimation of SsO has become a particularly challenging topic.To solve this issue,this paper proposes an improved spectrum analysis method by improving the window function and a spectrum correction method to achieve higher precision.First,by aiming at the sidelobe characteristics of the window function as evaluation criteria,a combined cosine function is optimized using a genetic algorithm(GA).Furthermore,the obtained window function is self-convolved to extend its excellent characteristics,which have better performance in reducing mutual interference from other SSO modes.Subsequently,a new form of interpolated all-phase fast Fourier transform(IpApFFT)using the optimized window function is proposed to estimate the parameters of SsO.This method allows for phase-unbiased estimation while maintaining algorithmic simplicity and expedience.The performance of the pro-posed method is demonstrated under various conditions,com-pared with other estimation methods.Simulation results validate the effectiveness and superiority of the proposed method.

可扩展架构的超大点数FFT处理器设计

面向合成孔径雷达、遥感、电子对抗等领域研究了一款高性能的超大点数快速傅里叶变换(FFT)处理器。文中提出了一种可扩展架构,即针对不同的应用场景可以动态实时调整FFT算法的基数以及处理点数;存储器划分为16个存储模块,可以通过产生无冲突地址进行访问,输出与输入数据帧可以共享同一存储器,具备高效存储器特征。FFT运算采用并行流水线排布,当采用高基算法时,可高并行度访问存储器,实现并行计算,从而获得明显的实时性优势。FFT各级运算采用循环移位寄存器产生地址,以保证蝶算单元输入数据的抽取间隔,并在最后一级输出时进行循环移位寄存器反转操作产生地址,实现输入输出共享存储器。所提设计方法规整、高效、适用范围广泛,便于现场可编程逻辑器件以及集成电路实施,并且也将持续受益于存储器工艺的提升。

基于置零点窗函数的电力谐波FFT分析方法

基于快速傅里叶变换(fast Fourier transform,FFT)的电力谐波算法,受到栅栏效应与非同步采样频谱泄露的影响,测量精度有待进一步提高。加窗和插值修正算法是改善FFT谐波参数测量准确度的有效方法。文章在置零点余弦窗的旁瓣特性和多项拟合插值算法基础上,提出置零点余弦窗FFT的电力谐波分析方法。根据谐波特点设计不同的余弦窗函数,由于窗函数的设计具有灵活性,针对某一种窗函数的插值算法不再适用,因此给出了更具一般性的双谱线和三谱线插值修正公式,为基于FFT的谐波分析提供新的方法。对旁瓣特性以及各次谐波的频率、幅度、相位的测量算法进行仿真分析,通过与经典的Hanning窗、Nuttal窗、Rife-Vincent窗的比较验证了所提方法具有更高的谐波参数分析精度。

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.

基于FFT和Masking的实时语音通话降噪算法

针对语音通话质量的提升问题,提出一种基于快速傅里叶变换(Fast Fourier Transform,FFT)和Masking技术的实时语音通话降噪算法。首先,提出一个实时语音通话降噪的基本框架,并研究了帧分割、窗函数处理及FFT的数学原理。其次,阐述了基于人耳听觉特性的Masking方法及其在频域中的应用。最后,通过逆快速傅里叶变换(Inverse Fast Fourier Transform,IFFT)将信号转换回时域,并进行实验分析。实验结果表明,该降噪算法可以有效改善语音的清晰度和整体感知质量。

基于五项Rife-Vincent(Ⅰ)窗的四谱线插值FFT谐波分析方法

目前,在电力谐波分析中快速傅里叶变换(FFT)应用得最为广泛,但是在非同步采样时,应用该变换容易产生频谱泄漏,出现栅栏效应。为减小非同步采样对FFT的影响,对旁瓣峰值电平小且下降速率快的五项Rife-Vincent(Ⅰ)窗进行了分析,并将它应用于FFT算法中,提出了基于五项Rife-Vincent(Ⅰ)窗的四谱线插值FFT谐波检测算法。经过多项式函数的拟合,得到了简单实用的四谱线插值修正公式,使计算过程更为简单。结果表明,与Hanning窗、Nuttall窗和四项Rife-Vincent(Ⅰ)窗插值FFT相比,相同条件下,五项Rife-Vincent(Ⅰ)窗具有更高的准确度,其幅值相对误差EAh≤6.524×10-5%,相位相对误差Eφh≤7.751×10^(-3)%。

面向5G终端基带处理的高量化信噪比FFT加速器设计

针对第5代移动通信系统(5G)终端基带处理芯片的设计要求,本文提出一种基于新型块浮点(BFP)技术的快速傅里叶变换(FFT)加速器。为了降低FFT计算过程中的量化误差,本文实现了一种逐级迭代、动态调整共享指数的块浮点技术,并在此基础上,引入“银行家舍入规则”处理BFP尾数缩放过程中的舍入误差,进一步提高该加速器的整体精度。此外,为了实现5G基带连续FFT处理需求,本文还实现了一种无地址冲突的顺序访存机制。实验结果表明,该加速器从128点至4096点FFT处理的量化信噪比(SQNR)都超过75 dB,比未采用块浮点的方案高8~15 dB;与其他较优秀的设计相比,在高点数(2048点、4096点)上也有3 dB的优势。本文FFT加速器在TSMC 28 nm工艺库下综合显示,总面积为0.193 mm^(2),最高支持600 MHz时钟频率,计算4096点FFT平均功耗为16.3 mW。

大点数FFT的工程案例

快速傅里叶变换(FFT)是“数字信号处理”课程中的重要知识点,该算法工程应用非常广泛。但FFT算法的推导过程比较复杂,学生不太容易深刻领会并灵活运用。以某型多频连续波雷达的数据处理为例,介绍如何利用16K缓存的芯片来实现128K点的FFT运算,通过实际工程案例来加深学生对FFT算法的理解,提高学生解决工程问题的能力。

基于FFT和三次Hermite插值的人体触电判据初探

针对当前基于TT系统(电气设备的金属外壳直接接地的保护系统)的低电压配电网输电线路上的剩余电流保护设备无法保证人触电后马上动作的现状,首先搭建活体触电试验平台,通过单相电压有效值220 V、频率50 Hz的电源对猪表皮进行触电试验,并使用控制变量的方法研究触电波形和触电面积、触电湿度以及触电时漏电电流大小之间的关系,得到试验数据;其次,对试验数据进行处理,使用FFT计算触电时刻的谐波畸变率,使用三次Hermite插值算法,绘制触电波形包络线,计算包络线不同时刻的斜率;最后,选择谐波畸变率最小值和合适的斜率,搭建仿真平台,对试验数据拟合得到的人体阻抗进行触电仿真,使用谐波畸变率和波形峰值斜率变化作为剩余电流保护设备触电判断依据,验证了所提判据的可行性。

多路并行流水线型基2^(2)FFT算法实现

FFT算法作为OFDM系统的核心算子占用其系统处理的大多数时间,为提高OFDM系统数据传输速度,提出了一种改进的多路并行流水线型基2^(2)FFT实现架构。在实现过程中着重对旋转因子的存储进行片上缓存优化,减少了乘法运算次数从而减小整体运算复杂度;设计的数据整合模块用于控制时序,从而保证P路并行流水型架构正确实现,数据运算吞吐率成P倍提高。RTL仿真结果表明,与同类架构相比,提出的架构在硬件开销适中的同时使得性能分别提升了1.27%、2.04%、50.88%,并且具有FFT点数可扩展的特点,可满足随着通信标准的不断提高,FFT点数逐渐增大的实际应用需求。

一种高速2-D滑动FFT的设计实现

文章介绍了采用2-D快速傅里叶变换(fast Fourier transform,FFT)算法的滑动窗FFT的基本特性原理和硬件实现过程,完成了窗长256点、步长16点的2-D滑动窗FFT的专用集成电路(application specific integrated circuit,ASIC)设计。传统FFT算法受序列完整性的制约,时滞较大,无法满足某些高实时性信号分析领域的处理速度要求。该文采用滑动FFT算法,克服了传统FFT对序列完整性的依赖,设计的滑动FFT处理器使用2-D FFT压缩新序列计算时间,以基16蝶形运算器为核心,采用系数复用和高基Booth方法优化系数编码技术压缩乘法器的数量,减少电路面积。所设计的2-D滑动FFT完成单次滑动窗长的计算时间比传统算法节约了16.1%,变换结果与MATLAB的运算结果相比,信噪比(signal-to-noise ratio,SNR)大于130 dB。在TSMC 28 nm的工艺下,工作主频为600 MHz,面积为1980μm×2060μm。