## Fourier Spectrum(傅里叶谱)研究综述

Fourier Spectrum 傅里叶谱 - We show that given a bound on the k-th level of the Fourier spectrum, one can construct a PRG with a seed length whose quality scales with k.^{[1]}It allows any image to be reconstructed by acquiring its Fourier spectrum by using a single-pixel detector.

^{[2]}By comparing the acceleration response of the soil and pipeline, monitoring the soil displacement, and analyzing the acceleration coefficient and Fourier spectrum, the seismic response characteristics of the soil at different excitation modes and peak seismic acceleration and its laws were investigated.

^{[3]}The Fourier spectrum of the Shubnikov–de Haas oscillations at atmospheric pressure contains two fundamental frequencies, namely, Fα ≈ 860 T and Fβ ≈ 4400 T, with cyclotron masses mα ≈ 1.

^{[4]}Fourier spectrum and wave envelope analysis showed that both algorithms have maintained the original non-stationary characteristics.

^{[5]}The site amplification curves and S-wave quality factor Qs(f) are determined and further utilized to correct the Fourier spectrum of earthquake records.

^{[6]}Raw temporal measurement, Fourier spectrum, envelope spectrum, and spectrogram input types are individually used to train CNNs.

^{[7]}In order to reveal the dynamic response from several aspects, four methods, including the Fourier spectrum, the horizontal-to-vertical spectral ratio (HVSR), the response acceleration, and the Arias intensity, were employed.

^{[8]}This method, with no need to select the seed waves, mainly uses the ratio of the Fourier spectrum of the combined vibration waveform and the single hole vibration waveform to quantify the suppressed vibration.

^{[9]}For this it is necessary to divide the Fourier spectrum of the sampled image by a factor depending on the selected aperture.

^{[10]}In this paper, different from most adversarial attacks which directly modify pixels in spatial domain, we propose a novel black-box attack in frequency domain, named as f-mixup, based on the property of natural images and perception disparity between human-visual system (HVS) and convolutional neural networks (CNNs): First, natural images tend to have the bulk of their Fourier spectrums concentrated on the low frequency domain; Second, HVS is much less sensitive to high frequencies while CNNs can utilize both low and high frequency information to make predictions.

^{[11]}Firstly, the volley surface structure dominated in the slope tends to magnify the vibration, resulting in intensive vibration of the soil body on the slide surface and an increased high frequency components of Fourier spectrum.

^{[12]}the Fourier spectrum and structure function.

^{[13]}Customarily, the MRS literature reports on fitting some ad hoc mathematical expressions to a set of resonances in a Fourier spectrum to extract their positions, widths and heights.

^{[14]}It showed clearly the chaotic behaviors through time response, phase diagram, Fourier spectrum, Poincaré section, bifurcation diagrams, and Lyapunov exponents.

^{[15]}In this study, given a set of observed motions, ground-motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables.

^{[16]}The regularity of a suitable sampling of the PRNU image is considered and it is measured through the decay of its Fourier spectrum.

^{[17]}The artifacts are caused by the incompleteness of these data, which, in turn, is due to cutting off the high frequencies of the Fourier spectrum.

^{[18]}The Fourier spectrum of the wind field over the western tropical Pacific is characterised by a large variety of peaks distributed from intra-seasonal to decadal time scales, suggesting that WWBs could be a result of nonlinear interactions on these time scales.

^{[19]}The Fourier spectrum is employed to analyze the energy transfer process between two traveling waves.

^{[20]}According to the properties of Fourier transform, Fourier single-pixel imaging uses the illumination lights with cosine distributions to obtain the Fourier spectrum of the object, and then apply the inverse Fourier transform to reconstruct the spatial information of the object.

^{[21]}Additionally, we demonstrate experimentally the ability to control the formation of emerging patterns by sculpting the Fourier spectrum of the optical system.

^{[22]}The water holdup data are acquired by conductance rings sensor, and processed by the improved empirical wavelet transform (EWT) to obtain the Fourier spectrum in the frequency domain and decomposition components in the multiscale domain.

^{[23]}In this paper, we propose a correspondence FGI scheme, which reconstructs the object's Fourier spectrum by averaging partial reference patterns corresponding to object-arm detection values of high fluctuations.

^{[24]}Due to the higher complexity of the Fourier spectrum, the original method would generate a large number of boundaries, more invalid components.

^{[25]}The proposed work uses the magnitude and phase of the Fourier Spectrum and the entropy of the image to defend against AE.

^{[26]}Fourier spectrum, coaxiality, and main thrust surface inner diameter change were selected as deformation evaluation indicators to comprehensively evaluate cylinder liner deformation.

^{[27]}In this paper, the validity of the constant-mass approximation is examined by comparing the Fourier spectrum of Brownian motions described by the Thiele equation and the Landau-LifshitzGilbert equation.

^{[28]}In the suggested method, the Itakura–Saito distance, which is a measurement of the similarity of stationary signals and based on Fourier spectrums, is modified by applying Kaiser filter onto short-time signals.

^{[29]}In terms of the Fourier spectrum of the relative intensity noise (RIN), we characterize the noise features of the MTCC-VCSEL in the ultra-high bandwidth domain.

^{[30]}Firstly, the Yule–Walker algorithm-based auto-power spectrum and Fourier spectrum were jointly adopted to segment the frequency bands of structural dynamic response data.

^{[31]}After collecting the ASW signals generated during laser ablation, we split the Fourier spectrum of the measured ASW into six equal bands and used each as an input for principal component analysis (PCA).

^{[32]}

我们表明，给定傅里叶谱第 k 级的界限，可以构造一个种子长度与质量成比例的 PRG。

^{[1]}它允许通过使用单像素检测器获取其傅里叶光谱来重建任何图像。

^{[2]}通过比较土壤和管道的加速度响应、监测土壤位移、分析加速度系数和傅里叶谱，研究了不同激发模式和峰值地震加速度下土壤的地震响应特性及其规律。

^{[3]}大气压下 Shubnikov-de Haas 振荡的傅里叶谱包含两个基本频率，即 Fα ≈ 860 T 和 Fβ ≈ 4400 T，回旋加速器质量 mα ≈ 1。

^{[4]}傅里叶频谱和波包络分析表明，两种算法都保持了原有的非平稳特性。

^{[5]}现场放大曲线和 S 波品质因数 Qs(f) 被确定并进一步用于校正地震记录的傅里叶谱。

^{[6]}原始时间测量、傅里叶谱、包络谱和谱图输入类型分别用于训练 CNN。

^{[7]}为了从多个方面揭示动态响应，采用了傅里叶谱、水平垂直谱比（HVSR）、响应加速度和Arias强度四种方法。

^{[8]}该方法无需选择种子波，主要利用组合振动波形的傅里叶谱与单孔振动波形的比值来量化抑制的振动。

^{[9]}为此，有必要根据所选孔径将采样图像的傅立叶光谱除以一个因子。

^{[10]}在本文中，与大多数直接修改空间域像素的对抗性攻击不同，我们基于自然图像的属性和人视觉系统之间的感知差异，提出了一种新的频域黑盒攻击，称为f-mixup。 (HVS) 和卷积神经网络 (CNN)：首先，自然图像的大部分傅里叶频谱往往集中在低频域；其次，HVS 对高频不太敏感，而 CNN 可以同时利用低频和高频信息进行预测。

^{[11]}首先，以斜坡为主的截击面结构容易放大振动，导致滑面土体强烈振动，傅里叶谱高频分量增加。

^{[12]}傅里叶谱和结构函数。

^{[13]}通常，MRS 文献报道了将一些特别的数学表达式拟合到傅立叶光谱中的一组共振，以提取它们的位置、宽度和高度。

^{[14]}它通过时间响应、相图、傅里叶谱、庞加莱截面、分岔图和李雅普诺夫指数清楚地显示了混沌行为。

^{[15]}在这项研究中，给定一组观察到的运动，使用高斯过程回归 (GPR) 方法构建目标站点的地面运动时间序列，该方法将傅里叶谱的实部和虚部视为随机高斯变量。

^{[16]}考虑到 PRNU 图像的适当采样的规律性，并通过其傅里叶光谱的衰减来测量。

^{[17]}这些伪影是由这些数据的不完整性引起的，而这又是由于切断了傅里叶光谱的高频。

^{[18]}热带西太平洋风场的傅里叶谱的特点是从季节内到年代际时间尺度上分布着各种各样的峰，这表明 WWB 可能是这些时间尺度上非线性相互作用的结果。

^{[19]}傅里叶谱用于分析两个行波之间的能量传递过程。

^{[20]}根据傅里叶变换的性质，傅里叶单像素成像利用具有余弦分布的照明光获得物体的傅里叶光谱，然后应用傅里叶逆变换重构物体的空间信息。

^{[21]}此外，我们通过雕刻光学系统的傅里叶光谱，通过实验证明了控制新兴图案形成的能力。

^{[22]}持水率数据通过电导环传感器获取，经过改进的经验小波变换（EWT）处理，得到频域的傅里叶谱和多尺度域的分解分量。

^{[23]}在本文中，我们提出了一种对应的 FGI 方案，该方案通过对与高波动的对象臂检测值相对应的部分参考模式进行平均来重建对象的傅里叶谱。

^{[24]}由于傅里叶谱的复杂度较高，原始方法会产生大量的边界，更多的无效分量。

^{[25]}所提出的工作使用傅里叶光谱的幅度和相位以及图像的熵来防御 AE。

^{[26]}选取傅里叶谱、同轴度、主推力面内径变化作为变形评价指标，对缸套变形进行综合评价。

^{[27]}在本文中，通过比较由 Thiele 方程和 Landau-LifshitzGilbert 方程描述的布朗运动的傅立叶谱来检验恒定质量近似的有效性。

^{[28]}在建议的方法中，通过对短时信号应用 Kaiser 滤波器来修改 Itakura-Saito 距离，它是对静止信号相似性的测量并基于傅里叶谱。

^{[29]}在相对强度噪声（RIN）的傅里叶谱方面，我们表征了 MTCC-VCSEL 在超高带宽域的噪声特征。

^{[30]}首先，联合采用基于 Yule-Walker 算法的自功率谱和傅里叶谱对结构动力响应数据的频带进行分割。

^{[31]}在收集激光烧蚀过程中产生的 ASW 信号后，我们将测量的 ASW 的傅里叶光谱分成六个相等的波段，并将每个波段用作主成分分析 (PCA) 的输入。

^{[32]}

## Nonlinear Fourier Spectrum 非线性傅里叶谱

Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network which we coined NFT-Net.^{[1]}The propagation of nonlinear waves is well-described by a number of integrable models leading to the concept of the scattering data also known as the nonlinear Fourier spectrum.

^{[2]}We evaluate improvement in the performance of the optical transmission systems operating with the continuous nonlinear Fourier spectrum by the artificial neural network equalisers installed at the receiver end.

^{[3]}In our work, we demonstrate a hardware implementation of the fast direct NFT operation: it is used to map the optical signal onto its nonlinear Fourier spectrum, i.

^{[4]}

我们的重点是计算与衰减轮廓相关的连续非线性傅里叶谱的未探索问题，使用我们创造了 NFT-Net 的特殊结构的深度神经网络。

^{[1]}<p>许多可积分模型很好地描述了非线性波的传播，这些模型导致了散射数据的概念，也称为非线性傅里叶谱。

^{[2]}nan

^{[3]}nan

^{[4]}

## fourier spectrum analysi 傅里叶谱分析

In order to extract rich features of flow regimes, empirical wavelet transform (EWT) and Fourier spectrum analysis are used to process the signals.^{[1]}Considering that the bushings are operating under Multiple-Frequency Voltage and Current Harmonics, a superposition analysis method is established for voltage and current with five frequencies based on a Fourier spectrum analysis of the rated voltage waveform and full-load current waveform.

^{[2]}Two-point space–time correlation and Fourier spectrum analysis are applied to large-eddy simulation results of a compressible parallel jet flow at Reynolds number 2000 and Mach number 0.

^{[3]}Based on global classical solutions and Fourier spectrum analysis, we obtain the optimal time-decay rates of global classical solutions in two and three space dimensions.

^{[4]}This study used observation data measured at several constructions at the West Sea in Ca Mau province in Vietnam and applied Fourier spectrum analysis method to deeply investigate the structure and propagation process of wave spectrum and its variation in amplitude and shape under the impact of centrifugal concrete embankment in the tidal area.

^{[5]}68 close to the Kolmogorov spectrum is detected through Fourier spectrum analysis, which indicates that the sub-daily fluctuations of GHI are nonstationary.

^{[6]}An interferogram processing algorithm which adopts the sum-of-squared-difference image registration method and Fourier spectrum analysis has been proposed to locate the centroid of each out-of-focus pattern and extract the spatial frequency of fringes, and subsequently particle position and size.

^{[7]}

为了提取流态的丰富特征，经验小波变换（EWT）和傅里叶谱分析被用来处理信号。

^{[1]}考虑到套管工作在多频电压电流谐波下，在对额定电压波形和满载电流波形进行傅里叶频谱分析的基础上，建立了五频电压电流叠加分析方法。

^{[2]}将两点时空相关和傅里叶谱分析应用于雷诺数为 2000 和马赫数为 0 的可压缩平行射流的大涡模拟结果。

^{[3]}基于全局经典解和傅里叶谱分析，我们得到了全局经典解在二维和三维空间维度上的最佳时间衰减率。

^{[4]}本研究利用越南金瓯省西海多个建筑实测数据，运用傅里叶谱分析方法，深入研究离心混凝土路堤冲击下波谱的结构和传播过程及其振幅和形状的变化。在潮汐区。

^{[5]}nan

^{[6]}nan

^{[7]}

## fourier spectrum analyzer

The issues of robotization of dairy cattle feeding and fodder quality control with the use of Fourier spectrum analyzers have been discussed.^{[1]}The performances of the antireflection microstructures were measured using an infrared Fourier spectrum analyzer and the best samples demonstrated $>99\%$>99% transmission in the 4.

^{[2]}

讨论了使用傅立叶频谱分析仪实现奶牛饲喂和饲料质量控制的机器人化问题。

^{[1]}nan

^{[2]}

## fourier spectrum show

Fourier spectrum shows that rotating instability and rotating stall both happened under the stall condition, and the frequency band of rotating instability does not change with the flow rate.^{[1]}The Fourier spectrum shows low-order p-modes and high-order g-mode pulsations that very likely stem from the F-type primary component star, which could be classified as a new δ Sct-γ Dor hybrid.

^{[2]}

傅里叶谱表明，在失速条件下，旋转失稳和失速均发生，旋转失稳的频带不随流量变化。

^{[1]}nan

^{[2]}