求解电路传输响应函数

熊猫羊

用Fourier变换的 时域积分性质 ,int (-inf,t) f(τ)dτ=F(w)/jw + πF(0)δ(w), 令f(τ)=δ(t),F(w)=1,


Fourier变换的 时域积分性质 见 页面
http://www.dolc.de/forum/viewthr ... &extra=page%3D1

熊猫羊

如果不用这个性质,直接求,即,int (0,+int) exp(-jwτ)dτ好像要用到 复变的围道积分, 具体的步骤了我都忘了,如需我可以以后答复
最后提醒一句,Dirac delta函数,及其任意阶导数,任意阶积分(含Heavyside阶梯函数,即你所求的这个函数) 的都不是经典意义上的函数,而是分布Distribution,它们的Fourier变换也非经典意义上的Fourier变换,因为它们都不满足经典Fourier变换的前提

熊猫羊

这种推广了的Fourier变换是为了满足工程的要求,但是存在一定问题,如所谓的Gibbs现象(如,11%振荡),就是在不满足经典Fourier变换的位置上的"奇异"现象

青蓝忘情水

谢谢PANDA学习了，刚才我邻居来也跟我一起讨论了半天这个问题，然后越讨论越乱，明天决定跟教授去聊聊看，我的思路是不是正确

eisenstange

又看了一下你的题目，发现几个问题，

首先通常我们说的系统传输函数，是指一个双口网络，两端的电压比，而你说的电流／电压比实际上导纳函数而不是系统的传输函数。

其次，题目要你求的是U(F)=fft(u(t))，实际上是输入信号的傅里叶变化。

青蓝忘情水

刚才跟教授沟通过了，是他跟我说错了，要求的系统传输函数应该是输出电压跟输入电压比，还有一个问题也是我刚才跟他讨论结果他又说是这样一个RLC串连然后加入一个阶约相应为1的电压源然后看体统时域的状况，他说电路可以是任意的其实电压源也可以是任意的，但正确的方法只有一种，然后让我再时域分析，然后在NUMERISCHANALYSEN

青蓝忘情水

还有这个问题用MATLAB怎样实现呢？$郁闷$

eisenstange

meiner Meinung nach mit differenzieller Gleichung 2er Ordnung.

熊猫羊

http://rapidshare.com/files/2196 ... withMATLAB_muya.rar
eBook:Solving ODEs with MATLAB

Solving ODEs with MATLAB

L. F. Shampine, I. Gladwell, S. Thompson
ISBN: 0521530946 | Publisher: Cambridge University Press (2003) | Publication Date: 2003-04-28 | Number Of Pages: 272 | PDF | 1,2 MB


Book Description
This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems. Each chapter begins with a discussion of the "facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understaning the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

青蓝忘情水

谢谢楼上两位，今天一个上午终于解出来了，很繁琐得，算了好几页，而且情况比较负责，因为我这里有两个ENERGIESPEICHERN，下步就是用MATLAB把这个问题再解一遍比较结果，教授说用MATLAB算出来得结果应该误差比较大，所以让我用手算，最后比较