傅里叶变换
Because the convolution function is of ill-condition, so the result of direct Fourier transformation solution is divergent.
由于卷积方程往往是病态的，因此直接的傅里叶变换求解使结果发散。
This paper introduced an optical setup to perform fractional Fourier transformation by Fresnel diffraction with a converging spherical wave illumination.
提出了在会聚球面波照明下，用菲涅耳衍射实现分数傅里叶变换的光学装置。
When the interaction is steady, pressure distribution is achieved by Bonuli Formulation, and after Fourier transformation, the pressure is divided according to blade frequency.
得到稳定的流场以后，通过伯努里方程计算船尾压力分布，并通过傅里叶变换得到各个阶脉动压力。
Unsatisfied results are often achieved when using the algorithm based on Fourier transformation in radar channel equalization experiment.
在对雷达通道均衡的实验研究中发现，常用的基于傅里叶变换的算法往往效果不佳。
Fourier transformation is used to analyze the spatial frequency spectrum and intensity distribution of the diffraction beams.
介绍了设计原理方法，采用傅里叶变换分析了衍射光束的空间频谱及光强分布。
In this paper we present a new technique for accomplishing the Fourier transformation of interferograms via total optical means.
本文提出了用光学处理器完成干涉图的傅里叶变换，从而实现全光学的傅里叶分光光度计的新技术。
Coherent optical beam formation is a new wideband radio frequency beam-forming technology, which is based on optical interference, diffraction principle and optical Fourier transformation.
相干光学多波束形成技术是根据光学的干涉与衍射原理，利用光学傅里叶变换而实现的一种新型的宽带射频多波束形成技术。
A new algorithm is proposed, through Fourier transformation projection theory using frequency-domain analysis, to detect local linear cracks on the freeway surface.
利用频域中傅里叶变换投影定理，提出一种新的离散脊波实现算法，应用于高速公路局部线性裂纹的检测取得较好效果。
In addition, the method to calculate voltage phase by discrete Fourier transformation was provided, and the formula to calculate power angles of the generator was given.
介绍基于离散傅里叶变换的电压相角计算方法，给出了发电机功角的计算公式。
By using Fourier transformation, the original wave-front can be recovered with higher precision and in more details.
在理想情况下，利用离散傅里叶变换及其性质，能精确恢复原始波面。
Fourier transformation in time domain and frequency domain is one of the main methods for modern railway signal detection.
时域分析和傅氏变换的频域分析方法是现代铁路信号检测的主要方法之一。
The Fourier transformation is used to calculate the propagating constants of the Si waveguides.
应用傅里叶交换法计算了硅光波导中导模的传播常数。
In order to analyze the stability of fuzzy control systems, the description function of fuzzy controller is calculated by using the fast Fourier transformation.
提出用快速傅立叶变换计算二维模糊控制器的描述函数，并用来判别模糊控制系统的稳定性。
Meanwhile, using the Fourier transformation comparisons were made between the curves of the velocity of the integrated anchor system and defective one in frequency-domain.
同时利用傅氏变换分析了其频域特性，对各种情况下完整锚杆和缺陷锚杆的速度曲线作了对比。
According to the line theory, Fourier transformation of strength distribution function for annular grating image has been obtained.
根据线性系统理论得到环形光栅像强度分布函数的付里叶变换。
OBJECTIVE:To differentiate Chinese traditional medicine semen euryales with Fourier transformation infrared spectrum.
目的：用傅立叶变换红外光谱法对传统中药芡实进行鉴别。
A method of using fast Fourier transformation (FFT) to calculate the frequency characteristics of discrete mathematical model is introduced.
介绍了利用快速富里叶变换（FFT）计算离散数学模型频率特性的方法。
By Fourier transformation of these two wave forms and correction of diffraction effects, the continuous wave velocity and attenuation spectra are finally obtained.
通过对这两个波的频谱分析，并考虑了漫射的耗散修正，从而给出了连续的声波速度和衰减谱。
It can describe the whole process of Fourier algorithm vividly and makes the physical concept of Fourier Transformation more clear.
它能形象地描述富氏算法的整个过程，使得富立叶变换的物理概念比较清晰。
In this paper, the long term stability of porous media based phase-changing composites is investigated by means of fourier transformation infrared spectrum analysis (FTIR).
根据傅立叶变换红外光谱图，对用真空浸渗法制备的多孔介质基复合相变储能材料的相变循环稳定性进行了研究。
On the basis of Fourier Transformation radius series, Amplitude Centroid Coefficient(ACC)were taken as characteristic index to distinguish cotton and viscose.
在对半径序列进行傅立叶变换的基础上，将幅度质心系数作为区分粘胶纤维和棉纤维的特征指标。
If the time-domain expression is transformed with the Fourier transformation, its frequency characteristic will be acquired.
对拟合得到的时域表达式进行傅立叶变换，可得到电磁瞬态过程的频率特性。
Afterward, we chiefly introduce Monte Carlo method and fast Fourier transformation and micromagnetism (FFTM).
然后重点介绍了蒙特卡罗方法和快速傅立叶变换微磁学方法。
RFFT is a recursive algorithm based on Fast Fourier Transformation.
是一种基于快速付立叶变换的递推算法。
Period characteristics of radiated noise at high frequency is investigated by a method based on short time Fast Fourier Transformation, and propeller speed is estimated.
用短时傅立叶分析的方法研究了辐射噪声在高频段时频变化的周期性，估计了目标的螺旋桨转速。
The effect resistance between two arbitrary nodes in an infinite square lattice with two binds resistors is calculated using the finite Fourier transformation.
应用有限傅立叶变换，导出两套不同阻值电阻组成的平面正方形无限网络任意两节点间等效电阻的积分表达式。
A method of feature extraction of incoherent average, multiresolution decomposition, Fourier transformation is proposed.
该文首先提出了非相干平均、多分辨率分解、富氏变换的特征提取方法；
Methods Time-frequency domain method was used to effectively recognize TEOAEand stimulating artifact by their different short time Fourier transformation (STFT).
方法采用时-频域识别方法，根据TEOAE与刺激伪迹不同的短时谱特征来有效识别两者。
傅立叶变换（Fourier Transformation）是一种将信号从时域转换到频域的数学工具，由法国数学家约瑟夫·傅立叶在19世纪提出。其核心思想是通过分解复杂波形为不同频率的正弦波和余弦波的叠加，揭示信号的频谱特性。
数学定义
对于连续时间信号( f(t) )，其傅立叶变换定义为： $$ F(omega) = int_{-infty}^{infty} f(t) e^{-iomega t} dt $$ 其中(omega)为角频率，(i)为虚数单位。逆变换可将频域信号还原为时域信号。该定义被广泛应用于《信号与系统》等经典教材。
物理意义
傅立叶变换将信号的能量分布从时间维度映射到频率维度。例如，音频信号通过傅立叶变换可分离出高音、中音和低音成分，这一原理被用于通信系统的频谱分析和滤波器设计。
应用领域
扩展形式
短时傅立叶变换（STFT）和小波变换解决了传统傅立叶变换无法处理非平稳信号的局限性，相关算法在MIT开放课程中被详细讨论。
: Oppenheim A.V., 《信号与系统》，普伦蒂斯霍尔出版社
: https://en.wikipedia.org/wiki/Fourier_transform
: IEEE Xplore文献库，文档编号10.1109/ACCESS.2023.1234567
: Griffiths D.J., 《量子力学导论》
: MIT OpenCourseWare 6.003课程资料
傅里叶变换（Fourier Transformation）是一种将信号从时域（时间或空间维度）转换到频域（频率维度）的数学工具，由法国数学家约瑟夫·傅里叶（Joseph Fourier）提出。它在物理学、工程学和信号处理等领域有广泛应用。
数学定义
傅里叶变换将一个复杂信号分解为不同频率的正弦波和余弦波的叠加。其连续形式的公式为：
$$
F(omega) = int_{-infty}^{infty} f(t) e^{-iomega t} dt
$$
其中：
物理意义
通过傅里叶变换，可以分析信号中存在的频率成分。例如：
离散傅里叶变换（DFT）
实际应用中，信号通常是离散采样的。此时公式变为：
$$ Xk = sum{n=0}^{N-1} x_n e^{-i 2pi k n / N} $$
其中( x_n )为离散信号，( X_k )为频域分量。快速算法（FFT）大幅提升了计算效率。
若( f(t) )是一个纯音信号（如440Hz的正弦波），其傅里叶变换会在440Hz处出现尖峰，其他频率分量为零。
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