Fourier series Definition and 706 Threads

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 :( [SIZE="4"]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...

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 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...

Looking for Fourier series tutorials or even better video lectures on the subject.

[SOLVED] Fourier series Homework Statement Hi. Please take a look at: https://www.physicsforums.com/showthread.php?t=104306 It is part 1 (finding the Fourier-series for f(x) = |x|) I am having trouble with. The Attempt at a Solution Ok, I can write f(x) = |x| for -pi =< x < pi as: f(x) =...

Hey everyone, I got the following Fourier series F.S f(x)= (pi/2) - (4/pi) \sumn=1,3.. to infinity (1/n^2 cos (nx)) l= pi After deriving it the question now is how can i use it to show \sum n=1 to infinity (1/(2n-1)^2= 1+ 1/3^2 + 1/5^2 +... = pi^2/8 I think I am not sure what...

Can someone fill in the blank between these two steps? I can't find Fourier series proof anywhere and my professor just left it out. (1) y(t+nT)=y(t) (2) y(t)=A_{0} + \Sigma^{\infty}_{n=1}[A_{n}cos(n\omegat) + B_{n}sin(n\omegat)] (The omega is going crazy on me... it's not supposed to...

HI, I really need to find a relationship between the coefficients of the Fourier transform coefficients and those for Fourier series, especially how to find Fourier series coefficients from the Fourier transform coefficients. The teacher talks about this in class but wants us to find the...

Homework Statement Is there a way to prove that E={sin(nx), cos(nx): n in N u {0}} is a maximal orthonormal basis for the Hilbert space L²([0,2pi], R) of square integrable functions (actually the equivalence classes "modulo equal almost everywhere" of the square integrable functions)? I...

Homework Statement For 0</= x </= pi, let f(x) be defined by f(x) = { A for [x - pi/2] < alpha { 0 for alpha </= [x-pi/2]</= pi/2 Where A and alpha are positive constants with alpha <pi/2. I have used </ to represent less than or equal to. The square brackets are to...

First off, this is not a homework problem. I was reading Charles Kittel solid states book on Chapter 2, equation 3: electron number density, n(x), expanded in a Fourier series: n(x) = n_0 + \sum_{p} [C_p cos(\frac{2\pi p x}{a}) + S_p sin(\frac{2\pi p x}{a})] From this expansion, wouldn't...

Homework Statement Find the term a2 in the following Fourier seies: [4+5 (cos x )^2]^(1/2) dx= ao + a2 cos (2x) + a4 cos (4x) The Attempt at a Solution The only thing I can think about is transforming that to complex numbers but I am not completely sure... I know that a0 is...

Homework Statement Consider F(t) = sin(wt) when 0 < t < pi/w and 0 when pi/w < t < 2pi/w. Where w is the frequency and t is the time. Find the Fourier Series Homework Equations F(t) = sum of (ck e^ikt) See attached doc with math type; its a lot more readable. The Attempt...

Hi, I have a question about Fourier Series(FS) in my textbook which is persentted like this: The uniqueness of a FS means that if we can find the FS of a waveform, we are assured that there is no other waveform with that FS, except for waveforms differing from the waveform under...

Homework Statement For the periodic signal x(t)\,=\,2\,+\,\frac{1}{2}\,cos\left(t\,+\,45^{\circ}\right)\,+\,2\,cos\left(3\,t\right)\,-\,2\,sin\left(4\,t\,+\,30^{\circ}\right) Find the exponential Fourier series.Homework Equations Euler’s Formula...

hey guys, I got this question that I am a bit stuck on. I have done question two and got the Fourier series, but have no idea how to do part 3. Any help is very appreciated. http://img453.imageshack.us/img453/5103/file2yp2.jpg

Homework Statement Write f(t) = 1 + t as Fourier series, with only cosine terms in the interval [0,pi] For which values of t does the series converge to f ? The Attempt at a Solution Expand f = 1+t as an even function about t=0; so it will be a zig-zag with non continuous points...

Homework Statement Let f be a periodic function with period 2pi Let: g = e^{2it}f(t-3) Find a relation between f and g's complex Fourier coefficents. Homework Equations y(t) = \sum _{n-\infty}^{\infty} b_n e^{in\Omega t} T \Omega = 2\pi T is period b_n =...

I know it's trivial...but how do you find the Fourier series of sin(x) itself? I seem to get everything going to zero...

I hope that this is the appropriate forum to ask something about Fourier series. My question is a little intuitive.Say I expand a function in Fourier series with n=-∞ to n=∞.The graph of the function is available. Now suppose,I cut off some terms for which |n|>N and expand the function.It...

Homework Statement Using the complex representation of Fourier series, find the Fourier coefficients of the periodic function shown below. Hence, sketch the magnitude and phase spectra for the first five terms of the series, indicating clearly the spectral lines and their magnitudes...

hi peeps. just a quick one. (a) how would you go around working out the Fourier for exponential functions.. simply something like e^x? (b) and how can this be applied to work out Fourier series for cosh and sinh (considering cosh = e^x + e^-x / 2) etc etc.. first of all.. is e^x even or...

Hi, I am having trouble understanding how to use Fourier series. To be more specific, here's what I mean. My question about those formulas is, how do I know what f(t) is? When I do excercises, I never get what f(t) is. Can anyone tell me how to find it?

When you compute the Fourier series coefficients for a function, is there any quick way to check if your answer is correct or at least reasonable?Thanks.

Hi, I'm looking for a recommendation for a good textbook which will deepen my understanding of intermediate/advanced mathematics to help me understand the above two (well I know one is subsection of the other) subjects. I would like to learn Fourier series for use with musical exploits. I...

Hello... How can I find an appropriate 'periodic' function (associated with a Fourier series) to derive the following 2 sums? 1. \displaystyle \sum_{k=1}^{\infty} \,\,\, \frac{\coth{(\pi k)}}{k^{3}} \,\,\, = \,\,\, \frac{7 \pi^{3}}{180} 2. \displaystyle \sum_{k=1}^{\infty} \,\,\...

to find the sum of a Fourier series...? My problem is: I must find the sum of ((-1)^(n+1))/2n-1 between infinity and n=1. I have looked in all my available textbooks for a clear example but I am still unsure as to how i should approach the problem? Help with this would be much...

Fourier series is a way to express a periodic function as a sum of complex exponentials or sines and cosines.. Is there actually a proof for the fact tat a periodic function can be split up into sines and cosines or complex exponentials?

Homework Statement Find the Fourier Series Expansion for: (a) f(x) = [pi-2x, 0 < x < pi | pi+2x, -pi < x < 0] (b) f(x) = [0, -pi < x < 0 | sin(x), 0 < x < pi]Homework Equations F(x)=\frac{a_0}{2}+\Sigma_{n=1}^{\infty}[a_ncos(nx)+b_nsin(nx)] a_0=\frac{1}{\pi} \int_{- \pi}^{\pi}f(x)dx a_n=...

Homework Statement Use the Fourier series technique to show that the following series sum to the quantities shown: \sum_{n=1}^\infty \frac{1}{n^4}=\frac{\pi^4}{90} 1+\frac{1}{3^2}+\frac{1}{5^2}+...=\frac{\pi^2}{8} Homework Equations I know the Riemann-Zeta function is \zeta...

Homework Statement if \nabla^2u = 0 in 0 \leq x \leq \pi, 0\leq y \leq \pi, boundary conditions u(0,y)=0, u(\pi,y)=cos^2y, u_y(x,0) = u_y(x,\pi)=0 Homework Equations I am required to show that u(x,y) = \frac{x}{2\pi} + \frac{cos2ysinh2x}{2sinh2\pi} The Attempt at a...

I have some problems on 'for' and 'while' loop so I could not write a MATLAB program for this question; . Well, how can I start?

I am expanding the function f(t) = e^{i \omega t} from (-π,π) as a complex Fourier series where w is not an integer. I am stuck figuring out how the series expands with n. c_n = \frac{1}{2 \pi} \int_{-\pi}^{\pi} e^{i \omega t} e^{-int} dt Join exponentials c_n = \frac{1}{2 \pi}...

Hi. I've been trying to find some material about Fourier Series in 2-D, along with 2-D Orthogonal Systems, but i haven't been able to find any about the former in any of the books i have (Toslov and Butkov's Mathematical Physics) nor online (nothing on mathworld?). Any input would be appreciated.

Hi there, I am a music student and have no math background whatsoever but was wondering if you guys could help me with something that I read in a book on signal processing. I want to create a periodic waveform that is described by the following Fourier series...

I get how to do them, I just have one question. An example that my prof. handed out has this: With the f(x) being 0 from -pi to 0, 1 from 0 to pi/2 and 0 from pi/2 to pi. But my question is when he has the last line in that picture. He has e^-ipi -> 1? I'm not understanding that step he's...

I'm confused. Trying to find the Fourier series of (sinx)^3. This is an odd function, so I try to find the Fourier sine coefficient, with integral of (sinx)^3*sinkx. However, my answer comes up with all sine terms. Of course all these terms go to zero when integrating between 0 and pi. Am...

Could someone please help me understanding this. Let f(x) = 0, -2< x <0 and x, 0< x <2 f(x) repeats this pattern for all x a) What is the period of f(x)? b) Is f(x) even, odd, or neither? c) Find the Fourier Series for f(x). a) I found that the period is 2 b) odd c) I'm not even sure...

I understand what the Fourier Theorem means, as well as how it behaves, I just don't understand how the math actually pans out or in what order to do what. I'm going to start off with what I know. f(x) = \frac{a_0}{2} \sum_{n=1}^{\infty}(a_n}\cos{nx} + b_{n}\sin{nx}) while, a_{0} =...

Can someone explain this to me simply. I just plain do not get Fourier Series. I've got a question that says: show that f(x)=exp(-cx) for 0<x<pi =exp(cx) for -pi<x<0 can be written as a cosine series that's way too complicated for me to work out how to write here. I have no idea...

Ok we are given the ODE {y}^{\prime\prime}(t) + \omega^2{y(t)} = {r(t)} r(t) = cos\omega{t} \omega = 0.5,0.8,1.1,1.5,5.0,10.0 I know you can use variation of paramaters to solve for it so I start by finding the complementary solution. {y}^{\prime\prime}(t) + \omega^2{y(t)} = 0...

Hey all, I am unsure how to do this problem... i find problems where i have to derive things quite difficult! :P http://img143.imageshack.us/img143/744/picture2ao8.png this is the Full Fourier series i think and so the Fourier coeffiecients would be given by...

A rectangular pulse train with peak-to-peak amplitude A = 2V (peak amplitudes are +/- 1V), period T0 = 1ms, pulse width a = 0.5ms, dc offset zero volt. How do you find the dBV of the one-sided Fourier coefficients cn for 0 ≤ n ≤ 12? n refers to the harmonic #? Is the Fourier coefficient...