Fourier series Definition and 706 Threads

Hello, I have a problem synthesising the complex Fourier series using Matlab. The time domain periodic function is: -1, -1.0 ≤ t < -0.5 1 , -0.5≤ t <0.5 -1, 0.5 ≤ t < 1 The single non zero coefficient is: Cn = \frac{2}{\pi n}, Co is 0 (average is 0). f(t)= \sum Cn...

Homework Statement Hey, the question i have been given reads: By a simple change of variables, show that if g(x) is a periodic real valued function with period L it can be represented as g(x)~ ∑∞n=-∞ An exp(-2\piinx/L) where the complex constants An are given by LAm =[L/2,-L/2]...

I believe this is an error minimization problem so I am trying to solve the following equation Min((∑ ( (S(t) - A cos(b t + C)))^2 ) Where S(t) is the input signal, t is time and I will sum over t, A is the amplitude, b is radians per second (frequency), and C is the phase angle. I...

Homework Statement For he following Fourier series, which of the answers correctly describes the following function y(t) = 2 - \stackrel{1}{π}∑1inf1/nsin(n*πt/2) a) odd function, period = 2 s b) Even function, period = 2s c) Odd function, period = 4s d) Even functio, period = 4s...

Homework Statement V(t) = 4 for 0<t< 1 and 0 for 1<t<3 and repeats itself for all t (negative and positive) Find the first 5 harmonics of the Fourier series in cosine form and find the power if this is the voltage over 100 ohm resistor The Attempt at a Solutionpower = d_dc ^2 / R + .5sum...

Is correct to define Fourier series like: f(t)=\sum_{k=0}^{\infty}a_k \cos \left (\frac{2 \pi k t}{T} \right ) + b_k \sin \left (\frac{2 \pi k t}{T} \right ) Where ak and bk: a_k=\frac{1}{T} \int_{-T}^{+T} f(t) \cos \left (\frac{2 \pi k t}{T} \right ) dt b_k=\frac{1}{T}...

Homework Statement x(t) = 4 for 0 <x<1 and 0 otherwise and this process repeats for all values including negative. find X_0 and X_n and find the first 6th harmonics of the Fourier series in cosine form Homework Equations The Attempt at a Solution x_0 = 4/3 x_n =...

Homework Statement This is a general question, no real problem statement and is connected to solving Fourier series. You know that to solve it, you need to find a_{n}, a_{0} and b_{n}. Homework Equations When solving the above mentioned ''coefficients'' you can get a solution with sin or...

Homework Statement Which of the signals is not the result of Fourier series expansion? options : (a) 2cos(t) + 3 cos(3t) (b) 2cos(\pit) + 7cos(t) (c) cos(t) + 0.5 Homework Equations Dirichlet conditionsThe Attempt at a Solution From observation, I thought all are periodic and so must be...

Homework Statement Consider the square wave function defined by y(t) = h (constant) when 0 ≤ (t + nT) ≤1, y(t) = 0 elsewhere, where T = 2 is the period of the function. Determine the Fourier series expansion for y(t). Homework Equations Fourier Analysis Coefficients The Attempt...

Simple question; Why isn't it \sum am (from m=1 to infinity) Thanks in advance.

Find the Fourier series solution to the differential equation x"+x=t It's given that x(0)=x(1)=0 So, I'm trying to find a Fourier serie to x(t) and f(t)=t, and I'm know it must a serie of sin... So here's my question...the limits of integration to the Bn, how do I define them? Will...

Homework Statement In "oppgave 4" http://www.math.ntnu.no/emner/TMA4120/2011h/xoppgaver/tma4120-2010h.pdf you have a periodic function which is NOT periodic from ##x=-L=-\pi## to ##x=L=\pi##, but at ##x=0## and ends at ##x=2 \pi=2L##. The formulas I have (like these...

Homework Statement https://wiki.math.ntnu.no/_media/tma4120/2013h/tma4120_h11.pdf Check out the solution to problem 4b) My question is: Why do they set ##b_n = \frac{2}{\pi} \int_{0}^{\pi}(...)dx## instead of ##b_n = \frac{1}{\pi} \int_{0}^{\pi} (...)dx##? Ie, why did they multiply the...

Hi! Which is the better method for finding Fourier expansions of a function? The ordinary one (find a_0, b_n and a_n with separate integrals), or the one which uses complex numbers (just find c_n)?

Homework Statement Hello guys, I have problem with the Fourier series, since we had only one lecture about it and I cannot find anything similar to my problem in internet. should we consider for the first f(x+1) integrated from -1 to 0 ? http://img819.imageshack.us/img819/3508/wbve.jpg when...

In finding Cn, I arrived at a different answer. I got an extra factor of (1/i) instead, which came when you do the integral of each exponential with respect to t; so you get a factor of 1/i(1-n) and 1/i(1+n) respectively.. Did they intentionally leave that out?

Hello, Find the Fourier serie of f(x)=|sin(x)| on the interval (-1,1) I'm just a little confused, does that mean that I have to integrate from -1 to 1 to find the coefficients ? Because the formula of the coefficients is in terms of the period T, for this function the period is pi. Or do I...

Homework Statement In the dirac notation, inner product of <f|g> is given by ∫f(x)*g(x) dx. Why is there a 1/∏ attached to each coefficient an, which is simply the inner product of f and that particular basis vector: <cn|f>? Homework Equations The Attempt at a Solution

I recently had an asignment where i calculated the Fourier series coefficients for f= 1+t for t= -1 to 0 f= 1-t for t=0-1 basically triangle looking. And as i summed more and more coefficients my function started looking more like this triangle (which was really cool). My question...

Homework Statement Determine the Fourier series for the full-wave rectifier defined as f(t) = sinωt for 0 < ωt < pi -sinωt for -pi < ωt < 0Homework Equations The Attempt at a Solution This looks like an even function, so bm = 0 Ao = 1/pi∫sinωt from 0 to pi = 1/pi(-cos(ωt))/ω) from 0 to...

Good morning everyone, I am taking a signals and systems course where we are now studying the Fourier series. I understand that this is for signals that are periodic. But I get hung up when determining the Fourier coefficients. In the video by Alan Oppenheim, he derives the equation for...

Homework Statement #35 on this page Homework Equations Integral of a series can be assumed to be the sum of integrals The Attempt at a Solution Picture of Work I am not sure where to proceed from here, advice?

http://en.wikipedia.org/wiki/Dirac_comb Please have a look at the Fourier Series section, and its last equation. Let T = 1. After expanding the Equation x(t) = 1 + 2cos(2∏t) + 2cos(4∏t) + 2cos(6∏t) ... Now this does not give the original Dirac Comb. Eg: at t = 1/2 x(1/2) = 0 But RHS =...

Is there some properties I should be aware of? after making the relevant substitutions, I ended up with $2 = 1 + \sum\nolimits_{m=0}^\infty \frac{4}{(2m+1)\pi}\sin(\frac{(2m+1)\pi}{2})$ but I can't get past this

I've just started learning Fourier series and I'm having trouble understanding it. What do they actually do? And what does the amplitude-frequency show me? I'm asking as a rookie in signal analysis, so if you could explain it to me as simple as you can it will be of great help. Thanks!

Sorry if I am posting in the wrong place. I'm really interested in the Fourier series, but I'm not an expert on it yet. I am very well aware yoy can do it with sound waves, but can you manipulate any other waves? What about light waves? And for absorption, how can you measure the...

Homework Statement An oscillator with free period \tau is critically damped and subjected to a force with the saw-tooth form \F(t)=c(t-n\tau) for (n-0.5)\tau<t<(n+0.5)\tau for each integer n. Find the amplitudes a_n of oscillation at the angular frequencies 2\pi n/\tau if c is a...

Homework Statement The problem: Justify the following equalities: \cot x = i\coth (ix) = i \sum^\infty_{n=-\infty} \frac{ix}{(ix)^2+(n\pi)^2}=\sum^\infty_{n=-\infty}\frac{x}{x^2+(n\pi)^2} I am trying to figure out how to start this. When I insert the Euler identity of \coth (using...

Hi all my first post as I need to seek help! I have just learned some simple Fourier series stuff and would like to be able to plot my answers in matlab. Assuming this is correct I was wondering if someone would be able to walk me through plotting this equation in Matlab...

Homework Statement The problem/question is attached in the file called "homework". In the third signal (the peridic rectangular wave), I am requested (sub-question b) to find the Fourier series of the wave. Homework Equations The file called "solution" presents a detailed solution to the...

Odd & Even Functions (was thread "Fourier Series") Homework Statement determine if the functions below are odd even or neither: a) f(x)=x^2+2 b) f(x)=(x^2+2)tan(x^2) c) f(x) = (x^2+2)sin(x)tan(x^2)Homework Equations even - f(x) = f(-x) odd - f(-x)=-f(x) The Attempt at a Solution I've managed...

Homework Statement Determine the Fourier series for the periodic function of period 2∏ defined by: -2 when (-∏ ) ∠ x ∠ (-∏/2) f(x)= 2 when ( -∏/2) ∠ x ∠ (∏ /2) -2 when (∏/2) ∠ x ∠ (∏) how to start i?. I have already drawn it but what next. thank you...

Hey there! I'm trying to calculate the Fourier Series for sin2x on [-π, π] For a0 I found 1/2. (By determining the average value of the function on the interval) Since sin2x is even, I know that bn = 0. Now, for an.. The following link shows the integral I used to try to evaluate an...

Square Pulse Train Fourier Series help?? Homework Statement problem+directions below: Homework Equations ω=2\pif β=\frac{2\pi}{\lambda} The Attempt at a Solution Since the problem asks to make all time-dependent sinusoidal functions deal with x-direction, i don't think i need to...

Hey. I'm looking for a proof of: Theorem: If f \in C^1(\mathbb{T}), then the Fourier series converges to f uniformly (and hence also pointwise.) I have looked around for it, googled, etc, but I only found proofs which used theorem they did not prove. (Or I misunderstood what they said.) I'd...

Homework Statement Fourier coefficients: A_0=0, a_n=0, b_n=2/(n∏) ; period p=2 Homework Equations Fourier series The Attempt at a Solution Attempt was not good enough!

Hi, I wish to obtain the Fourier series of the signal in red (please see attached figure fig1_sine_plots.png). Basically, it is a full-wave rectified 3f sinusoid, where f = 50Hz. The blue signal represents a sinusoid with frequency f = 50Hz. In the following equations (please see attached...

Homework Statement (a) On (-π,π), find the Fourier series of f(x) = x. (b) Hence, or otherwise, find the Fourier series of g(x) = x2 (c) Hence, show that \sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90} Homework Equations f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} \left( a_n \cos \frac{n...

Hi! I was wondering how you would graph a Fourier series for a square wave that periodic. My textbook gave something proper that I would expect (just google 'Square Wave Fourier Series Expansion') while my TI - 84 gave a image like the one somewhere in this thread. It would be nice if anybody...

The Fourier series can be used to represent an arbitrary function within the interval from - π to + π even though function does not continue or repeat outside this interval. Outside this interval the Fourier series expression will repeat faithfully from period to period irrespective of whether...

The Fourier series can be used to represent an arbitrary function within the interval from - π to + π even though function does not continue or repeat outside this interval. Outside this interval the Fourier series expression will repeat faithfully from period to period irrespective of whether...

Homework Statement The function f(x) is defined by: f(x) = -1 when \pi < x <0 and 0 when 0<x<\pi Show that \sum^{∞}_{0}\frac{(-1)^n}{2n+1}=\frac{\pi}{4} Homework Equations Fourier series for a function of period 2\pi = a_{0} + \sum^{∞}_{1}a_{n}cos(nx) + b_{n}sin(nx)...

In a rigorous mathematical course I am talking, it seems to make a difference when I am given a function f and need to write its Fourier series, whether it is defined on [0,2∏] or [0,2∏). What difference does it make for my series whether it is an open or a closed interval?

Homework Statement Calculate the following integral: \int_{0}^{2\pi}(\sum_{k=0}^{\infty} \frac{\cos(kx)}{3^k})^2 dx Homework Equations Parseval's identity: \frac{1}{2 \pi} \int_{-\pi}^{\pi} {|f(x)|^2 dx} = \sum_{n=0}^{\infty} {|a_n|^2+|b_n|^2} Where a_n, and b_n are the trigonometric...

Homework Statement f(x) = 1, 0<x<1 Extend f(x) t generate an even function P(x) and find Fourier coefficients Homework Equations an = 2/T ∫ P(x)cos(2nx/T) dx The Attempt at a Solution P(x) = 1, -1<x<1 0, -2<x<-1 , 1<x<2 even function so b0 = 0 Average of P(x)...

Hey guys! if anyone can help me I guess it is you! :) I'm trying to find the Fourier Series demonstration to continuous and periodic functions. I don't understand why people keep using X(jw) and X[e^jw] and even sometimes X(w) and X(f) If anyone can help me I'm really not understanding that...

First, I've had to find the Fourier series of F(t) = |sin(t)|, which I've calculated as f(t) = \frac{2}{\pi} + \sum_{n=1}^{\infty}\frac{4cos(2nt)}{\pi-4\pi n^2} I'm pretty sure that's right, but now I need to evaluate the sum using the above Fourier series...

Homework Statement Find the Fourier coefficients for the function *Should be a piecewise function, not sure how to write one in [itex /itex] tags* f(x) = |x|, |x| < 1, 1, 1≤|x|< 2; f(x+4) = f(x) and Find the Fourier series for f(x) = cos1/2\pi x, -1≤x<1...

I have some rather technical questions about the complex exponential form of the Fourier series: 1) What is the motivation behind the complex exponential form? Why not just use the real form (i.e. with sine and cosines)? 2) Surely the complex exponential form is an orthogonal set, i.e...