Fourier series Definition and 706 Threads

My professor said the Fourier series of sinx*cosx is simply 0.5sin2x. Is this right?? Is there no summation?? I don't understand why .. Help!

Homework Statement sin(t)cos(nt) dt Homework Equations The Attempt at a Solution I tried setting u=sin(t) or cos(nt) or nt but none seems to work. Can someone give me a hint as what to set u equal to? Thanks.

Homework Statement Find the complex Fourier series for f(t)=t(1-t), 0<t<1 Homework Equations \sum_{n=-\infty}^{\infty}c_{n}e^{2in\pi t} where c_{n}=\int_{0}^{1}f(t)e^{-2in\pi t}dt The Attempt at a Solution I've worked out that c_{n}=-1/(2n^2 \pi^2). The problem is that for...

fourier series - trig and complex not matching? i am given a signal which can be written as: s(t) = -1 {-1 < t < 0}, 1 {0 < t < 1}, 0 {1 < t < 2} [it's a pulse train] the period, T, is 3. i have calculated the trig. Fourier series representation, which in MATLAB turns out to be correct...

Homework Statement Find the Fourier series for the function f(x) = 1/cos(x) on the segment [-pi/4, pi/4]. Homework Equations A Fourier series for a function f(x) with period 2L has the form: (a0/2) + SUM(n=0 to infinity) [ an*cos((n*pi*x)/L) + bn*sin((n*pi*x)/L) ], where...

Hi all, I couldn't find any proof of the following statement: The Fourier series expansion of f(x), which has a discontinuity at y, takes on the mean of the left and right limits i.e. f(y)= (1/2)(f(y+)+f(y-)) is there anyone who can help me? Thanks

Homework Statement find the Fourier series for the function 0 -pi<x<pi f(x)={ sinx 0<x<piHomework Equations The Attempt at a Solution I don't know how to do this and can't find a good explanation anywhere, any kind of help is appreciated...even just a push in the...

I'm trying to understand some MATLAB code. It's the Fourier series approximation of a signal. This is my first time using matlab, so I guess I'm really trying to comprehend the syntax. For my example, I am using some code I googled (http://www.ee.nmt.edu/~wedeward/EE341/FA97/example8.html)...

I was wondering what to do if I have a DE like this x'' + \omega^2x = \cos^2(t) \sin^2(t) I have to decide for what omega it has a solution with period 2pi. Now to solve this I have to find the Fourier series representation of the right hand side, but the problem is that I get all An...

That is what I know, what I'm after is what do I do if my limits are different? i.e I'm trying to do this in the interval of pi/4<x<3pi/4 obviously this isn't a case of -L<x<L So I can't have a coefficient of 1/L outside the integral, what is my coefficient?

Fourier series no.2 :) Homework Statement Hey guys. So I have this function f(x) between -pi and pi. I found the Fourier series for it. Now I need to find the Fourier series for g(x). The problem is, I'm not sure about g(x), is it correct what I did? Thanks in advance. Homework...

Fourier series summation...help! Basically, i need to show that... 2 + sum (m=1 to n) [4(-1)^m . cos(m.pi.x)] = 2(-1)^n.cos((n+1/2)pi.x)/cos((pi.x)/2) Any ideas?

hi i wanted to know if anybody that knew about dsp and all the Fourier series and transforms had any advice on how to master it ... very swiftly..

Homework Statement Question: Find the half-range Fourier sine series for the function f(t) = t sin(t) Problem: According to all the examples I have gone through, they all have a limit when asking for the half-range. However, my teacher, in the question posted above, has not specified any...

Homework Statement Please see attached image. From the given information, I am having trouble deriving the left and right hand limits, I just can't figure out what these are... http://img176.imageshack.us/img176/9334/fstih3.png Homework Equations None needed. The Attempt at a...

hello, i'm a self learner currently learning Fourier series. Anyway, I'm having some problem with a question regarding the inner product of two complex functions. This is defined by an integral from negative infi to positive infi of the multiplication of one function and the complex...

Homework Statement Test the convergence of the series for the surface charge density: \sum^{\infty}_{s=0}(-1)^s(4s+3)\frac{(2 s -1)!}{(2s)!} Homework Equations (2s-1)! = \frac{(2s)!}{2^s s!}; (2s)! = 2^s s! Stirling's asymptotic formula for the factorials: s! = \sqrt{2 \pi s}s^s...

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...

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: sinn[SIZE="4"]π=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...

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.