What is Fourier coefficients: Definition and 71 Discussions
In mathematics, a Fourier series () is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. With appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). As such, the summation is a synthesis of another function. The discrete-time Fourier transform is an example of Fourier series. The process of deriving weights that describe a given function is a form of Fourier analysis. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier transform and inverse transform.
Hey guys, I'm working on a MATLAB program to find Fourier coefficients.
The problem with it: it gives a graph that has a different period and amplitude than the original function (although its the same general shape).
I've uploaded a screenshot of the graph that I'm referring to (as an...
Homework Statement
suppose that we have the continuous time signal
x(t) = cos(4πt) with fundamental period of T=1/2Homework Equations
a_{k} = \frac{1}{T} \int_{T}{}x(t)e^{-j\omega_{0}kt}dt
where \omega_{0} is obviously \frac{2\pi}{1/2} = 4\pi
well the problem is that this integration...
I am trying to find the Fourier coefficients for the following signal:
For some reason, I keep getting 0, which doesn't make sense to me.
I am even getting 0 for F0 even though there is clearly area under the curve. Here's my work for this part:
Period = T/2
Natural freq = 4pi/T
F0 =...
Hello!
How do I prove
?
Thank you!
(it can be proven by using the convergence of the Fourier series in L_p-norm, but I want to use the above result to prove the convergence in L_2-norm, so I want to avoid that)
letsa say i have an ak = cos ( k*Pi/4) + sin(3*k*Pi/4), the signal is discrete time, fundamental period N=12.
the way i would derive its x[n] is.. Sum(k=0, to 11 of: 0.5*exp(j*k*Pi/4) *exp(j*k*w*n) + 0.5*exp(-j*k*Pi/4) *exp(j*k*w*n) + (1/2*j)*exp(j*k*3*Pi/4) *exp(j*k*w*n) -...
Homework Statement
Let f be a C1 function on [-pi,pi]. Prove the Fourier coefficients of f satisfy
|an| <= K/n and |bn| <= L/n n=1,2,...
Homework Equations
an = 1/pi * int[-pi..pi] (f(x)*cos(nx)) dx
bn = 1/pi * int[-pi..pi] (f(x)*sin(nx)) dx
Sorry if my form is slightly...
Homework Statement
Given the first cycle of a waveform:
f(t)=2u(t)-2u(t-1)+u(t-2)-u(t-3)
-- Plot the first cycle of the wave form
-- Find the Fourier Coefficients
Homework Equations
Given above
The Attempt at a Solution
No idea yet. Will appreciate any help.
Homework Statement
Hi i would just like some fast hints, I'm doing the integrals wrong, I am splitting up the integral below and get the wrong answer.
well it's about finding the Fourier series for f(t)={0 for -π<t<0 and sint for 0≤t≤π}
Homework Equations
a_{n} =...
Homework Statement
Determine the Fourier coefficients of the 3-periodic function and determine how many terms needed to keep 3 digit accuracy.
f(t) = 1/2(1-Cos[Pi t]), for 0<t<1
f(t) = 1, for 1<t<2
f(t) = 1/2(1-Cos[Pi(t-3)]), for 2<t<3
Homework Equations
For the cos...
Homework Statement
So I'm supposed to show that a finite Fourier approximation is the optimal approximation for a given function.
I am to suppose we have a given set of functions \phi _k(x),k=1,2,\text{...}N defined on a\leq x\leq b.
They are orthogonal \int _a^b\phi _m(x)\phi _n(x)dx=0...
Homework Statement
f(t) = 1 0<=t<T/2
-1 T/2 <=t<=T
ie. step function.frequency w_0 = 2pi/T
Homework Equations
The Attempt at a Solution
What's the definition for the Fourier coefficients a_n and b_n again? Not the one in wikipedia.
Homework Statement
f (x) = 0 -pi<x<0
x^2 0<x<pi
Find the Fourier series and use it to show that
(pi^2)/6=1+1/2^2+1/3^2+...
Homework Equations
N/A
The Attempt at a Solution
I was able to find the Fourier series and my answer matched with the back of the...
Hi,
I was wondering if it is possible to express the norm of a function in terms of Fourier coefficient. If so, how do you go through it if given a particular function.
Thanks
Homework Statement
1. f is a function defined on the interval -a<x<a and has Fourier coefficients an=0 bn=1/n^(1/2) what can you say about the integral from -a to a of f^2(x)dx?
2. Show that as n goes to infinity the Fourier sine coefficients of the function f(x)=1/x -pi<x<pi tend to a...
[SOLVED] Fourier coefficients
Homework Statement
For f \in C^{2\pi}\cap C^1[-\pi,\pi] , I have to show that
\sum_{n\in\mathbb{Z}}|c_n(f)| < \infty
where c_n(f) is the Fourier coefficient of f;
c_n(f) = (f, e_n) = \frac{1}{2\pi}\int_{-\pi}^{\pi} f(t)e^{-int}\,dt
f \in...
There are two functions f(t) and g(t); t is the independent variable.
The distance between the two functions will be given by [1/2pi integral{f(t)-g(t)}^2 dt]^1/2 between -pi and +pi.
Apparently, this distance also is the Fourier coefficient of each term in the Fourier
expansion of a...
A function f(t) can be represented by the expansion
f(t) = \frac{1}{2}A_{0} + A_{1}cos(\omega t) + A_{2}cos(2 \omega t) + A_{3}cos(3 \omega t) + ...
B_{1}sin(\omega t) + B_{2}sin(2 \omega t) + B_{3}sin(3 \omega t) + ...
Do the constants A_{n} and B_{n} the same thing as the real and...
Im just looking through examples of finding the Fourier coefficients.
in one particular example bn is found to be = (-1/npi) (cosnpi - cos 0)
then it says this is 0 when n is even
and 2/npi when n is odd
are we just substituting values of n e.g. 1,2,3... to find this result?
i...
Yes, another thread... lab due tomorrow :-p
We take the integral of the function f(t) times one of the components:
integral(0->T) of [a0 + sigma(n=1->N) acos(nwt) + bsin(nwt)]sin(nwt)
Now, in order to evaluate this is it correct to say we multiple sin(nwt) through then take the integral of...
I need to find the Fourier series for the function f(x)=x. I have come across trying to find the integral from -pi to pi of -ixSin(nx). How do I go about evaluating this integral when n is infinity? I seem to only be able to find integrals in an integral table where n is an integer, but not...
Hi!
I have to calculate the Fourier coefficients c_n = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}dx and the Fourier series for the following function:
f(x)=
\begin{cases}
\frac{2}{\pi}x + 2 & \text{for } x\in \left[-\pi,-\pi/2\right]\\
-\frac{2}{\pi}x & \text{for } x\in...