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fourier series

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fourier series 【數學】傅立葉級數。

【數學】傅立葉級數。 “fourier“ 中文翻譯：   n. 1.傅立葉〔姓氏〕。 2.Francois Mar ...“series“ 中文翻譯：   n. 〔sing., pl.〕 1.連續；系列。 2.套 ...“complete fourier series“ 中文翻譯：   完全傅立葉級數“complex fourier series“ 中文翻譯：   復合傅里葉級數“conjugate fourier series“ 中文翻譯：   共軛傅立葉級數“continuous-time fourier series“ 中文翻譯：   連續時間傅立葉級數“discrete fourier series“ 中文翻譯：   離散傅里葉級數“discrete-time fourier series“ 中文翻譯：   離散時間傅立葉級數“double fourier series“ 中文翻譯：   二重傅里葉級數“exponential fourier series“ 中文翻譯：   指數傅里葉級數“fourier bessel series“ 中文翻譯：   傅里葉 貝塞耳級數“fourier half-rang series“ 中文翻譯：   半幅傅里葉級數“fourier series shape analysis“ 中文翻譯：   傅里葉級數形態分析“fourier stieltjes series“ 中文翻譯：   傅里葉-司蒂吉斯級數“fourier-bessel series“ 中文翻譯：   傅里葉-貝塞耳級數“fourier-legendre series“ 中文翻譯：   傅里葉-勒讓德級數“fourierreihe fourier series“ 中文翻譯：   傅里葉級數“fs，fourier series“ 中文翻譯：   傅里葉級數“generalized fourier series“ 中文翻譯：   廣義傅里葉級數“multiple fourier series“ 中文翻譯：   多重傅里葉級數“discrete-time fourier series pair“ 中文翻譯：   離散時間傅立葉級數對“fourier“ 中文翻譯：   n. 1.傅立葉〔姓氏〕。 2.Francois Marie Charles Fourier 弗朗瓦斯馬利沙利傅立葉〔1772-1837，法國空想社會主義者〕。 3.Jean Fourier 季恩傅立葉〔1768-1830，法國數學家，物理學家〕。 “a series of“ 中文翻譯：   一系列,一連串; 一系列..., 一批..; 一系列的“in series“ 中文翻譯：   串聯電路的，成串聯的; 電串聯的; 連續地, 串聯“in series with“ 中文翻譯：   串聯; 與...相連

fourierism

Through the analysis of the dynamic characteristic of geomagnetic intensity in a orbit , the magnetic dipoles produced by magnetorquer are expanded in fourier series . the new method of momentum unloading is educed according to the need of the sum of unloaded momentum , and the magnetic dipoles are figured out under the theory of optimal control 通過對在軌衛星地磁場強度的變化規律分析，將衛星磁力矩器產生的磁矩按富利哀級數展開，根據衛星所需卸載角動量大小，按照最優控制理論求出三軸磁矩取值，得到一種新的利用地磁場給飛輪卸載的方法。

In this paper , dynamic stability of parametrically excited flexible cam - follower system on the weakly nonlinear condition is investigated by using the combination of both the method of multiple scales and the technique of fourier series expansion . the equations of approximate transition curves in the plane of the dimensionless frequency and excitation ( amplitude ) parameter that separate stable from unstable solution are derived 隨后，本文采用多尺度法并結合fourier級數展開，分析了不同的凸輪從動件運動規律和不同的凸輪的升程、停程以及回程的時間分配規律下，無間隙的周期時變凸輪系統模型的穩定性，獲得了各種規律下的凸輪系統的穩定區間圖。

[ 5 ] expressed the wavefunction in terms of a two - dimensional fourier series . this form can satisfy the continuity of the function and of its derivative divided by the band - mass . but the number of the terms is so large that it is difficult to calculate the physical magnitudes in the single quantum wire 1996年， s . gangopadhyay等人將波函數用二維傅立葉級數展開，這種取法滿足波函數的連續性條件及粒子流( 1 / m ~ * ) ' ( x , y )的守恒條件，但是當考查單量子線時，需要展開的項數很多，計算量很大。

One dimensional equation can be obtained through extending the stream function and forcing term into fourier series , and this equation can be solved by assuming the traveling - wave solution . besides converting the topographies to flat bottom , the transforms also change the distribution of forcing . for subcritical topography , the intensity of 所用的求解方法為將解和強迫項在變換平面內進行付里葉級數展開，得到一維的波動方程，通過設行波解的方法求解該一維波動方程，所有模態解的疊加即為內潮生成問題的解。

Finally , to consider the effect of the compression of the approach embankment to the determination of the tolerable differential settlement , this paper , considering the flexible pavement as viscoelastic multilayers and dividing the moving traffic load into fourier series , presents the formulation and the application of a combination of transfer matrix and laplace transform and fourier transform approach to evaluate dynamic response of the flexible pavement subjected to a moving traffic load under modified plain - strain condition . the predictive capability of the model are verified by the laboratory model 為了考慮車路耦合對路橋過渡段容許差異沉降確定的影響，本文將柔性路面視作粘彈性體層狀體系，采用修正的平面應變模型，將移動的車輛荷載用傅立葉級數展開，用傳遞矩陣配拉氏變換和傅立葉變換法進行了移動荷載作用下柔性路面動力響應分析，并用模型試驗證明了理論分析結果的正確性。

Due to complicated continuous helicopter models and a wide range of constraints , numerical solutions on a mainframe computer have to take a long time . for a given set of initial helicopter states and flight parameters , optimal solutions are fitted by a fourier series . the coefficients of the fourier approximations are then interpolated as functions built by three - layer bp network with inputs of initial flight states and parameters 最后,由于直升機數學模型的復雜性,這給實時優化計算帶來很大困難,本文研究了地面計算機計算的最優軌跡如何在機載計算機上實時顯示,對飛行員的操縱提供參考,即把不同初始條件得到的最優軌跡曲線進行傅立葉部分級數化,得到傅立葉系數,選取合適初始條件作為變量,對這些最優軌跡曲線進行擬和,建立bp神經網絡預測模型。

Review of linear algebra , applications to networks , structures , and estimation , lagrange multipliers , differential equations of equilibrium , laplace ' s equation and potential flow , boundary - value problems , minimum principles and calculus of variations , fourier series , discrete fourier transform , convolution , applications 線性代數回顧，網絡，結構以及估計的應用，拉格朗日乘數，平衡態的微分方程，拉普拉斯方程和勢流，邊值問題，最小值原理和變分法，傅立葉級數，離散傅立葉變換，卷積，應用。

The obtained results in the paper are as follows : ( 1 ) the expansion of fourier series of orthogonal trigonometric polynomial for conditional mathematical expectation and function of random variable ; ( 2 ) the best approximation of trigonometric polynomial about another random variable for function of a random variable ; ( 3 ) the best approximation order of trigonometric polynomial for function of random variable 摘要獲得了如下結果： ( 1 )條件數學期望及隨機變量函數的三角多項式級數表達； ( 2 )一個隨機變量關于另一個隨機變量的三角多項式的最佳逼近； ( 3 )隨機變量函數被隨機變量三角多項式最佳逼近的階。

We construct eigenfunctions from the linear combination of the b - spline functions and the truncated fourier series , and extend pseudospectral method to calculate above - threshold ionization electron spectrum of one - dimensional atom in intense laser fields . our results are also in very good agreement with those of split - operator method 本文還利用b樣條函數和傅立葉級數的線性組合構造原子未微擾的本征函數，將偽譜方法推廣用來計算一維模型原子在強激光場中的閾上電離譜，其結果與分裂算符方法所得的結果也符合得很好。

We consider a neutral particle with magnetic moment antiparallel to the field . with the interaction potential energy between the magnetic moment of the particle and the magnetic field , we obtain the classical motion equation of the neutral particles in the loffe trap . in some limit conditions , by using the perturbative method , the equations may take on concise forms . of which the two equations about x and y are mathieu equations . if we properly set the parameters and have the condition a > > q > 0 , we can solve the mathieu equation with the traditional wkbj method . as a new attemptation , with fourier series expansion we solve the mathieu equation and obtain the classical motion law of the neutral particles 若阱的參數設置使得條件> > q 0成立時，我們可以利用傳統的wkbj方法近似求解馬丟方程。作為一種新的嘗試，本文還采用傅立葉級數展開的辦法來對馬丟方程進行求解，從而得到中性粒子在阱中的經典運動規律。在研究ioffe阱對中性粒子的囚禁問題時，實際上我們更感興趣的是馬丟方程的周期解，而要想獲得這種周期解，和q必須滿足一定的關系，亦即必須選擇阱的特定的參數和粒子的特定初始條件，對這一問題我們進行了嘗試性的研究。

The main results achieved in this thesis can be summarized as follows : 1 . by means of the fourier series expansion , an approximate analytical propagation equation of flattened gaussian beams ( fgbs ) passing through an apertured paraxial abcd optical system is derived , and illustrated with numerical examples , when the transmissivity of the aperture is t ( x ) = cos ( x ) 用傅立葉級數展開法研究了平頂高斯光束通過有光闌限制的近軸abcd光學系統的傳輸特性，導出了光闌透射率為t ( x ) = cos ( x )時的近似解析傳輸公式，硬邊光闌的情況可作為= 0的特例得到。

On the basis of the theory of thin shells and the non - moment assumption , the equations of motion of the cylindrical shells under longitudinal line - loading are derived in the case of ignoring the shearing stress , and then , the set of partial differential equations are solved by the fourier series method 基于薄殼理論和無矩假定，在略去剪切應力的情況下推導了圓柱殼在縱向線載荷作用下的運動方程，并采用fourier級數法進行了求解。

It induces the idea of pixel ' s 8 - neighbor fourier series , randomly chooses the local region of texture and computes the spectrum of it . after quantizing the spectrum , the spectrum histogram of the local area is extracted and then provided to the sofm network as a feature vector to train the net 引入象素的八近鄰付立葉級數，計算隨機選取的紋理區域的紋理譜并量化得到譜直方圖，將其作為sofm網絡的特征模式輸入并訓練網絡。

All kinds of the methods are proposed to estimate the nonparametric regression function , such as the kernel method , the local polynomial estimators , the smoothing spline , the series estimators ( b - spline estimator . fourier series estimator , wavelet series estimator ) 對于非參數回歸人們提出了許多估計方法，如核估計，局部多項式估計，光滑樣條估計，級數估計(傅里葉級數估計，小波級數估計)等。

Ordinary differential equation , first order differential equations , 2nd order differential equations , power series solution of differential equation , laplace transform , fourier series and transform , matrix , eigen value problem , partial differential equation 常微分方程式、一階微分方程式、二階微分方程式、微分方程式級數解、拉氏轉換、復利葉級數與轉換、矩陣、本徵值問題、偏微分程式。

The hard - edged aperture can be regarded as a special case of = 0 . 2 . by using the fourier series expansion , approximate analytical propagation equations of laser beams through a paraxial optical abcd system with different apertures are derived 用傅立葉級數展開法研究光束通過有光闌限制的近軸abcd光學系統的傳輸特性，導出了光闌透射率函數不同時的傳輸公式。

Based on the fourier series digital approximation method , the optimal design of flat - top and high isolation pass band frequency response interleaver has been studied . at last a solution of high isolation ( > 45db ) 用傅立葉級數展開數值逼近的方法進行了高隔離度平頂通帶頻響全光纖奇偶交錯濾波器的優化設計，提出了隔離度大于45db通帶平坦濾波器的制作方案。

With the fourier series technique , the disturbance is discomposed into predominant mode and high frequency harmonics . the nonlinear stability of three - dimensional disturbances for the blasius boundary layers is studied 借助fourier級數的方法將擾動波分解為基本模態和高頻模態,研究了三維擾動的非線性邊界層穩定性問題。

Furthermore , with the fourier series technique , the disturbance is discomposed into predominant mode and high frequency harmonics , and the nonlinear stability of the nonparallel boundary layer is studied 采用fourier級數的方法把擾動波分解為基本模態和高頻諧波模態,導出非平行非線性拋物化穩定性方程。