傅裡葉變換
Because the convolution function is of ill-condition, so the result of direct Fourier transformation solution is divergent.
由于卷積方程往往是病态的，因此直接的傅裡葉變換求解使結果發散。
This paper introduced an optical setup to perform fractional Fourier transformation by Fresnel diffraction with a converging spherical wave illumination.
提出了在會聚球面波照明下，用菲涅耳衍射實現分數傅裡葉變換的光學裝置。
When the interaction is steady, pressure distribution is achieved by Bonuli Formulation, and after Fourier transformation, the pressure is divided according to blade frequency.
得到穩定的流場以後，通過伯努裡方程計算船尾壓力分布，并通過傅裡葉變換得到各個階脈動壓力。
Unsatisfied results are often achieved when using the algorithm based on Fourier transformation in radar channel equalization experiment.
在對雷達通道均衡的實驗研究中發現，常用的基于傅裡葉變換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.
介紹了設計原理方法，采用傅裡葉變換分析了衍射光束的空間頻譜及光強分布。
In this paper we present a new technique for accomplishing the Fourier transformation of interferograms via total optical means.
本文提出了用光學處理器完成幹涉圖的傅裡葉變換，從而實現全光學的傅裡葉分光光度計的新技術。
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.
相幹光學多波束形成技術是根據光學的幹涉與衍射原理，利用光學傅裡葉變換而實現的一種新型的寬帶射頻多波束形成技術。
A new algorithm is proposed, through Fourier transformation projection theory using frequency-domain analysis, to detect local linear cracks on the freeway surface.
利用頻域中傅裡葉變換投影定理，提出一種新的離散脊波實現算法，應用于高速公路局部線性裂紋的檢測取得較好效果。
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.
介紹基于離散傅裡葉變換的電壓相角計算方法，給出了發電機功角的計算公式。
By using Fourier transformation, the original wave-front can be recovered with higher precision and in more details.
在理想情況下，利用離散傅裡葉變換及其性質，能精确恢複原始波面。
Fourier transformation in time domain and frequency domain is one of the main methods for modern railway signal detection.
時域分析和傅氏變換的頻域分析方法是現代鐵路信號檢測的主要方法之一。
The Fourier transformation is used to calculate the propagating constants of the Si waveguides.
應用傅裡葉交換法計算了矽光波導中導模的傳播常數。
In order to analyze the stability of fuzzy control systems, the description function of fuzzy controller is calculated by using the fast Fourier transformation.
提出用快速傅立葉變換計算二維模糊控制器的描述函數，并用來判别模糊控制系統的穩定性。
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.
同時利用傅氏變換分析了其頻域特性，對各種情況下完整錨杆和缺陷錨杆的速度曲線作了對比。
According to the line theory, Fourier transformation of strength distribution function for annular grating image has been obtained.
根據線性系統理論得到環形光栅像強度分布函數的付裡葉變換。
OBJECTIVE:To differentiate Chinese traditional medicine semen euryales with Fourier transformation infrared spectrum.
目的：用傅立葉變換紅外光譜法對傳統中藥芡實進行鑒别。
A method of using fast Fourier transformation (FFT) to calculate the frequency characteristics of discrete mathematical model is introduced.
介紹了利用快速富裡葉變換（FFT）計算離散數學模型頻率特性的方法。
By Fourier transformation of these two wave forms and correction of diffraction effects, the continuous wave velocity and attenuation spectra are finally obtained.
通過對這兩個波的頻譜分析，并考慮了漫射的耗散修正，從而給出了連續的聲波速度和衰減譜。
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個過程，使得富立葉變換的物理概念比較清晰。
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).
根據傅立葉變換紅外光譜圖，對用真空浸滲法制備的多孔介質基複合相變儲能材料的相變循環穩定性進行了研究。
On the basis of Fourier Transformation radius series, Amplitude Centroid Coefficient(ACC)were taken as characteristic index to distinguish cotton and viscose.
在對半徑序列進行傅立葉變換的基礎上，将幅度質心系數作為區分粘膠纖維和棉纖維的特征指标。
If the time-domain expression is transformed with the Fourier transformation, its frequency characteristic will be acquired.
對拟合得到的時域表達式進行傅立葉變換，可得到電磁瞬态過程的頻率特性。
Afterward, we chiefly introduce Monte Carlo method and fast Fourier transformation and micromagnetism (FFTM).
然後重點介紹了蒙特卡羅方法和快速傅立葉變換微磁學方法。
RFFT is a recursive algorithm based on Fast Fourier Transformation.
是一種基于快速付立葉變換的遞推算法。
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.
用短時傅立葉分析的方法研究了輻射噪聲在高頻段時頻變化的周期性，估計了目标的螺旋槳轉速。
The effect resistance between two arbitrary nodes in an infinite square lattice with two binds resistors is calculated using the finite Fourier transformation.
應用有限傅立葉變換，導出兩套不同阻值電阻組成的平面正方形無限網絡任意兩節點間等效電阻的積分表達式。
A method of feature extraction of incoherent average, multiresolution decomposition, Fourier transformation is proposed.
該文首先提出了非相幹平均、多分辨率分解、富氏變換的特征提取方法；
Methods Time-frequency domain method was used to effectively recognize TEOAEand stimulating artifact by their different short time Fourier transformation (STFT).
方法采用時-頻域識别方法，根據TEOAE與刺激僞迹不同的短時譜特征來有效識别兩者。
傅立葉變換（Fourier Transformation）是一種将信號從時域轉換到頻域的數學工具，由法國數學家約瑟夫·傅立葉在19世紀提出。其核心思想是通過分解複雜波形為不同頻率的正弦波和餘弦波的疊加，揭示信號的頻譜特性。
數學定義
對于連續時間信號( f(t) )，其傅立葉變換定義為： $$ F(omega) = int_{-infty}^{infty} f(t) e^{-iomega t} dt $$ 其中(omega)為角頻率，(i)為虛數單位。逆變換可将頻域信號還原為時域信號。該定義被廣泛應用于《信號與系統》等經典教材。
物理意義
傅立葉變換将信號的能量分布從時間維度映射到頻率維度。例如，音頻信號通過傅立葉變換可分離出高音、中音和低音成分，這一原理被用于通信系統的頻譜分析和濾波器設計。
應用領域
擴展形式
短時傅立葉變換（STFT）和小波變換解決了傳統傅立葉變換無法處理非平穩信號的局限性，相關算法在MIT開放課程中被詳細讨論。
: Oppenheim A.V., 《信號與系統》，普倫蒂斯霍爾出版社
: https://en.wikipedia.org/wiki/Fourier_transform
: IEEE Xplore文獻庫，文檔編號10.1109/ACCESS.2023.1234567
: Griffiths D.J., 《量子力學導論》
: MIT OpenCourseWare 6.003課程資料
傅裡葉變換（Fourier Transformation）是一種将信號從時域（時間或空間維度）轉換到頻域（頻率維度）的數學工具，由法國數學家約瑟夫·傅裡葉（Joseph Fourier）提出。它在物理學、工程學和信號處理等領域有廣泛應用。
數學定義
傅裡葉變換将一個複雜信號分解為不同頻率的正弦波和餘弦波的疊加。其連續形式的公式為：
$$
F(omega) = int_{-infty}^{infty} f(t) e^{-iomega t} dt
$$
其中：
物理意義
通過傅裡葉變換，可以分析信號中存在的頻率成分。例如：
離散傅裡葉變換（DFT）
實際應用中，信號通常是離散采樣的。此時公式變為：
$$ Xk = sum{n=0}^{N-1} x_n e^{-i 2pi k n / N} $$
其中( x_n )為離散信號，( X_k )為頻域分量。快速算法（FFT）大幅提升了計算效率。
若( f(t) )是一個純音信號（如440Hz的正弦波），其傅裡葉變換會在440Hz處出現尖峰，其他頻率分量為零。
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