Fourier series Definition and 750 Threads

a) Write a Matlab function, which accepts the following inputs -a finite set of Fourier series coefficients -the fundamental period T of the signal to be reconstructed -a vector t representing the times for which the signal will be reconstructed. This function should produce an...

Hello, I'm having some trouble completing a Fourier series question. We have f(x)=Cos(x), for abs(x)≤π/2 f(x)=0, for π/2≤abs(x)≤π period=2π and then show that the Fourier series f(x) reads http://img71.imageshack.us/img71/3424/84335314oi1.jpg now I can get the 1/π and the...

Homework Statement a) Write a Matlab function, which accepts the following inputs -a finite set of Fourier series coefficients -the fundamental period T of the signal to be reconstructed -a vector t representing the times for which the signal will be reconstructed Homework...

I never took complex analysis in undergrad and always regretted it, so I'm working through the book Visual Complex Analysis on my own. Really enjoying it so far. Homework Statement Actually you can view the problem...

Hey everybody! I am an undergrad student ,in an ee department.Ive taken "signals and systems" and two ago we got into the Fourier part. The question i have is whether or not there are some steps someone can follow in order to find the Fourier series given some specific graph.Now,our professor...

Homework Statement Recently in my signals class,we got to the chapter of Fourier series.We have learned that there are some basic graphs that can be described with Fourier series (sawtooth,square pulse etc) and so far i have understood their respective Fourier formulas.The problem i face...

Homework Statement Hi all. I have used Fourier series a lot in my maths study, and now I am about to use it when analyzing electrical circuits. In my notes from a lecture, I wrote down an example done by the professor. We are looking at a RCL-circuit with an applied EMF given by the periodic...

Fourier series ... Hi, everyone, I’m new to these forums. I’m just doing some work on Fourier analysis, and just have a few curious questions, I just need to clear up, and so I understand it better. I have been playing around with the java applet for Fourier series from this website...

Homework Statement f is integrable on the circle and satisfies the Lipschitz condition (Holder condition with a=1). Show that the series converges absolutely (and thus uniformly). i literally spent about 20 hours on this problem today but i just could not figure it out. i have a feeling...

Hello, I am currently dealing with Fourier Series, and a question about the period length of a product of two periodic functions is bothering me. If you have two different periodic functions with different (or the same) period and you sum them up, what happens to the period? Can this generally...

Homework Statement Given that the Fourier series of function f1(t) = At/π + A , -π < t < 0 = -At/π +A, 0 < t < π is f(t) = 0.5A +4A/π2(cos t + 1/9 cos 3t + 1/25 cos 5t + ...) what is the Fourier series of function f2(t) = -At/π, -π < t < 0 = At/π, 0 < t < π The Attempt at a...

Hello, I couldn't figure out the following problem so far. Homework Statement m,n \in \mathbb{N}. Show the following relations: Homework Equations a) is no problem, but b) and c) seem tricky. I tried partial integration (two times) on b), which gave me a term which contained the original...

Homework Statement find Fourier series for: sinnπ=0 (n=0,+1,-1,+2,-2...) I really can't understand how Fourier series works.. Like I tried solving problems..but till now, it didn't sink in my brain.. I just want 2 know the basic way of solving a problem regarding Fourier series..then...

Homework Statement (a) The negative half-cycles of a sinusoidal waveform E(t) = E0*cos(omega*t) are removed by a half- wave rectifier. Find the Fourier series representing the resulting wave in the output. (b) Find the output produced by a full-wave rectifier, which inverts...

Homework Statement Find the Fourier series corresponding to the following functions that are periodic over the interval [-\pi,\pi] f(x) = 1, -\pi/2 < x< \pi/2; f(x) otherwise. Homework Equations Fourier Series: f(x) = \frac{1}{2}a_0 + \sum^\infty_{n=1}a_n...

Hi, I'm trying to write a MATLAB Script to solve the Fourier series coefficients of a square wave via simultaneous equations in MATLAB. Any advice? I can write the expression out by hand, but cannot code it. Please advice.

Homework Statement Let f(x) be defined by the following Fourier series for \left|x\right|: f(x) = \frac{\pi}{2} - \frac{4}{\pi}\sum_{1,3,...}\frac{cos\left(nx\right)}{n^{2}} Show that \sum_{1,3,...}\frac{1}{n^{2}} = \frac{\pi^{2}}{8} and \sum_{1,2,3,...}\frac{1}{n^{2}} =...

The problem are as below :- f(x) = { x, for 0 < x < pi/2; x/2, for pi/2 < x < pi; pi-(x/2), for pi < x < 2*pi; how do I convert it to Matlab code and produce a graph of Fourier series with n=500? I have done analytically by hand for n=2, but the question ask to produce...

Homework Statement Hi all. Please take a look at the lowest equation in this picture: http://img143.imageshack.us/img143/744/picture2ao8.png This is Parselvals Identity. Let us say that I am given a Fourier series of f(x), and I want to calculate the integral of f(x)^2 from -L to...

Homework Statement Prove: f(t)=\sum_{i=1}^\infty (-1)^{n+1} \frac{Sin(n\omega t)}{n} represents the sawtooth function. Homework Equations Fourier Series Equations: f(t)=\frac{a_0}{2}+\sum_{i=0}^\infty \left(a_n Cos(nt)+b_n Sin(nt) \right) where a_n=\frac{2}{T}\int_{t}^{t+T} dt...

Homework Statement Hi all. There is an example in my book, where we have the following Fourier series, and the author writes it as: f(x) = \sum\limits_{n = 1}^\infty {\left( {\frac{{( - 1)^n }}{{n^2 }}\cos \left( {\frac{{n\pi x}}{p}} \right) + \frac{1}{n}\sin \left( {\frac{{n\pi...

I'm trying to find the Fourier series of |sin x| between -pi and pi. I've got it down to: a_n = \frac{1}{\pi} \int^{\pi}_{-\pi} |sin x| cos (nx) dx which i wrote as: a_n = \frac{2}{\pi}\int^{\pi}_0 sin x cos (nx) dx writing sin x cos (nx) = \frac{1}{2} (sin (n+1)x - sin (n-1)x) I...

Fourier series vs Integral: just one "coherent" notation? Hi all, notations for Fourier analysis always confuse me. I understand that the "volume" normalization factor can be disposed of either in the definition of the Fourier coefficient or in the definition of the Fourier series (or...

Why is the complex Fourier series expanded from +\infty to -\infty. Yet the regular Fourier series from 0 to +\infty?

Find the Fourier series of the 2Pi-periodic function f(x)= {0 , Abs(x) <= Pi/2 {Abs(x)-Pi/2, Pi/2 < Abs(x) <= Pi My attempt at a solution I have sketched the function... It equals zero between -Pi/2 and Pi/2 and it equals Pi/2 at -Pi and Pi. Then the...

Any one Solution will be appreciated , just solve as soon as possible! 1) Fourier Series 2) Heat Equation

Hi hows it going, Im currently doing a linear maths course, i suppose it'd be introductory. I am using Elementary Linear algebra by Howard anton and find that very good. However the course goes on to deal with laplace transforms and Fourier series, can anyone recommend a good (introductory)...

[b]1. Find Fourier Series Coefficient for a signal. (alternanate sawtooth pulse from t= -3 to 3 amplitude 1 on positivwe side and-1 on negative side. 3 pulse on positive side. 3 pulse on negative side. pulse width is 1.) as given in attachment file. [b]2. Compute the Fourier series...

Homework Statement Hi everyone. I have a Fourier series problem from an old Physics GRE that I would like to discuss. Here is a link to the problem and a solution. The answer they get is correct, but their explanation is not: http://grephysics.net/ans/9277/39Homework Equations Fourier...

Homework Statement The odd periodic function f(x) is defined by f(x) = -4-x for -4 <= x <= 0 and 4-x for 0 <= x <= 4 f(x + 8) = f(x) Sketch f(x) for -12 <= x <= 8 Find the coefficients in the Fourier series for the function defined by equation (1) and write out the series...

I'm trying to solve a basic heat equation \frac{\partial T}{\partial t}=\alpha \frac{\partial^2 T}{\partial x^2} I manage to get T=X(x)\tau(t) Then \tau(t)=A*e^{-\alpha*\lambda^2*t} and X(x)=C*sin(\lambda x) where \lambda=\pi/Ln n=1,2,3,... From here I don't know how or why I get to a...

May be simple, but I'm getting problem with doing Fourier series expansion of Sin(x) for -pi\leqx\leqpi

I can do the Fourier series but this question is really confusing F(x) is 1 for 0<x< pi , 0 for pi < x < 2pi and f(x+2pi) = f(x) for all x I know that it means that the period is 2pi and L = 2pi/2 = pi 1) Sketch f(x) for -4pi <x < 4pi I sketched the graph so that is alrite 2) Find...

fourier series, please help! Homework Statement Find the Fourier series of f(x)=(sin x)^2. Homework Equations The Attempt at a Solution I know that I need to use the double angle formulas for this problem: (sin x)^2=1/2-1/2(cos 2x) but I do not know where to go from here.

Use a Fourier series to prove that: \int_{0}^{ \infty} \frac{\sin(x)}{x}\ \mbox{d}x = \frac{ \pi}{2} What function do I need to Fourier transform?

fourier series pleeeease :( Hi every one, I want your help please. I have a difficulty in answering these questions. Actually it seems simple but I could not answer them because I did not understand the lesson very well. This homework worths 5% and I have to hand it as soon as...

Homework Statement if 0<\lambda<1 and f(x) = x for 0<x<\lambda\pi and f(x) = (\lambda/(1-\lambda))(\pi-x) for \lambda\pi<x<\pi show that f(x)= 2/(\pi(1-\lambda))\Sigma(sin( n\lambda\pi)sin(nx))/n^{}2 Homework Equations The Attempt at a Solution am i right in saying that...

Homework Statement if 0<\lambda<1 and f(x) = x for 0<x<\lambda\pi and f(x) = (\lambda/(1-\lambda))(\pi-x) for \lambda\pi<x<\pi show that f(x)= 2/(\pi(1-\lambda))\Sigma(sin( n\lambda\pi)sin(nx)(/n^{}2 Homework Equations The Attempt at a Solution am i right in saying that...

Homework Statement if 0<\lambda<1 and f(x) = x for 0<x<\lambda\pi and f(x) = (\lambda/(1-\lambda))(\pi-x) for \lambda\pi<x<\pi show that f(x)= 2/(\pi(1-\lambda))\Sigma(sin( n\lambda\pi)sin(nx)(/n^{}2 Homework Equations The Attempt at a Solution am i right in saying that...

Homework Statement if 0<\lambda<1 and f(x) = x for 0<x<\lambda\pi and f(x) = (\lambda/(1-\lambda))(\pi-x) for \lambda\pi<x<\pi show that f(x)= 2/(\pi(1-\lambda))\Sigma(sin( n\lambda\pi)sin(nx)(/n^{}2 Homework Equations The Attempt at a Solution am i right in saying that...

Homework Statement I need help finding the exponential Fourier series for the pulse train below. http://img329.imageshack.us/img329/1184/20080427091409ev5.jpg Homework Equations p_T(t)=\sum_{n=-\infty}^{\infty}{D_n e^{j2nt} D_n=\frac{1}{T_0}\int_{T_0}^{}{x(t)e^{-j2nt}dt}The Attempt at a...

Hey, I am trying to solve this question: obtain a Fourier series for a saw-tooth wave, a periodic signal, with period T, defined such that x(t)=At -T/2<= t >= T/2 where A has a value of 1 at the maximum value of x(t) i) obtain the Fourier series for this periodic signal in form...

[SOLVED] Fourier Series Homework Statement I know this may be a simple problem but I am just beginning to understand this subject and this question has confused me. Expand the following as a whole-range Fourier series: f(x) = 1 -pi < x < 0 f(x) = x 0 < x < pi I...

Homework Statement Having shown that: f(x) = e^{ax} = \frac{sinh(a\pi)}{\pi}\sum^{\infty}_{n=-\infty}\frac{(-1)^{n}(a+in)}{(a^{2}+n^{2})}e^{inx} on (-\pi,\pi) with 'a' a real constant Deduce that: \pi coth(a\pi) = \frac{1}{a} + \sum^{\infty}_{n=1}\frac{2a}{(a^{2}+n^{2})}...

Homework Statement Show that f is 2-pi periodic and analytic on the strip \vert Im(z) \vert < \eta, iff it has a Fourier expansion f(z) = \sum_{n = -\infty}^{\infty} a_{n}z^{n}, and that a_n = \frac{1}{2 \pi i} \int_{0}^{2\pi} e^{-inx}f(x) dx. Also, there's something about the lim sup of...

Homework Statement Solve \frac{1}{1} \int^{0}_{-1} -t e^{-j2\pi*nt}dtHomework Equations So I use integration by parts u = -t and dv = e^{-j2\pi*nt} , du= -1 and v = \frac{1}{-j2\pi*n}e^{-j2\pi*nt}The Attempt at a Solution after integration by parts I get: \frac{e^-j2\pi*nt}{j2pi*n} +...

[SOLVED] Fourier series and even/odd functions Homework Statement I found the solution to a PDE in this thread: https://www.physicsforums.com/showthread.php?t=224902 (not important) The solution is the sum of u(rho, phi) = [A_n*cos(n*phi)+B_n*sin(n*phi)]*rho^n. I have to find the general...

Use the Fourier series technique to show that the following series sum to the quantities shown: 1+1/3^2+1/5^2+...+1/n^2=pi^2/8 for n going to infinity I foudn the series to be: sum(1/(2n-1)^2,n,1,infinity) but I don't know how to prove the idenity. I don't know how to go about...

Use the Fourier series technique to show that the following series sum to the quantities shown: 1+1/3^2+1/5^2+...+1/n^2=pi^2/8 for n going to infinity I foudn the series to be: sum(1/(2n-1)^2,n,1,infinity) but I don't know how to prove the idenity. I don't know how to go about...

Homework Statement So I have to find the Fourier series for sin^{5}(x). Homework Equations I know the a_{n} in: \frac{a_{0}}{2} + \sum^{\infty}_{n=1}a_{n}cos_{n}x + \sum^{\infty}_{n=1}b_{n}sin_{n}x goes to zero, which leaves me with taking the b_{n}. The Attempt at a Solution So what I got...