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...