If given a set of data points for the magnitude of a cepheid variable at a certain time (JD), how can we use fourier series to find the period of the cepheid variable?
I'm trying to do a math investigation (IB math investigation) on finding the period of the cepheid variable M31_V1 from data...
Hello Everyone!
I want to learn about Fourier series (not Fourier transform), that is approximating a continuous periodic function with something like this ##a_0 \sum_{n=1}^{\infty} (a_n \cos nt + b_n \sin nt)##. I tried some videos and lecture notes that I could find with a google search but...
Homework Statement
Find the Fourier spectrum ##C_k## of the following function and draw it's graph:
Homework Equations
3. The Attempt at a Solution [/B]
I know that the complex Fourier coefficient of a rectangular impulse ##U## on an interval ##[-\frac{\tau}{2}, \frac{\tau}{2}]## is ##C_k =...
Homework Statement
Find the Fourier series of the function ##f## given by ##f(x) = 1##, ##|x| \geq \frac{\pi}{2}## and ##f(x) = 0##, ##|x| \leq \frac{\pi}{2}## over the interval ##[-\pi, \pi]##.
Homework Equations
From my lecture notes, the Fourier series is
##f(t) = \frac{a_0}{2}*1 +...
Homework Statement
There is a sawtooth function with u(t)=t-π.
Find the Fourier Series expansion in the form of
a0 + ∑αkcos(kt) + βksin(kt)
Homework Equations
a0 = ...
αk = ...
βk = ...
The Attempt at a Solution
After solving for a0, ak, and bk, I found that a0=0, ak=0, and bk=-2/k...
I'm kinda just hoping someone can look over my work and tell me if I'm solving the problem correctly. Since my final answer is very messy, I don't trust it.
1. Homework Statement
We're asked to find the Fourier series for the following function:
$$
f(\theta)=e^{−\alpha \lvert \theta \rvert}}...
Homework Statement
Considering the function $$f(x) = e^{-x}, x>0$$ and $$f(-x) = f(x)$$. I am trying to find the Fourier integral representation of f(x).
Homework Equations
$$f(x) = \int_0^\infty \left( A(\alpha)\cos\alpha x +B(\alpha) \sin\alpha x\right) d\alpha$$
$$A(\alpha) =...
Homework Statement
Consider the fourier series of a signal given by
$$x(t)=\sum_{k=-\infty}^{\infty} a_ke^{jk\omega_0t}$$
Let's consider an approaches to this series given by the truncated series.
$$x_N(t)=\sum_{k=-N}^{N} a_ke^{jk\omega_0t}$$
a- Show that if $x(t)$ is real then the series...
I'm trying to use Maxima to examine the error in a Fourier series as the number of terms increases. I've figured out how to produce a Fourier series and plot partial sums, but this has me stumped.
If anyone experienced with the Maxima CAS has some insight into this, I would greatly appreciate...
Homework Statement
f(x)=x on [0,2)
Homework Equations
Fourier Series is given as:
f(x)=a0/2 + n=1∞∑(an*cos(nπx/L) + bn*sin(nπx/L)
a0=1/L*-LL∫f(x)dx
The Attempt at a Solution
Basically what I am being taught is that we take the Period, T, to be equal to 2L so, T=2L
In this case T=2 and L=1...
Homework Statement
I am self studying an introductory quantum physics text by Marvin Chester Primer of Quantum Mechanics. I am stumped at a problem (1.10) on page 11. We are given
f(x) = \sqrt{ \frac{8}{3L} } cos^2 \left ( \frac {\pi}{L} x \right )
and asked to find its Fourier...
Homework Statement
I want to find the Fourier series of the sawtooth function in terms of real sine and cosine functions by using the formula:
$$f_p (t)=\sum^\infty_{k=-\infty} c_k \exp \left(j2\pi \frac{k}{T}t \right) \tag{1}$$
This gives the Fourier series of a periodic function, with the...
Homework Statement
Let ## f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) ##
What can be said about the coefficients ##a_n## and ##b_n## in the following cases?
a) f(x) = f(-x)
b) f(x) = - f(-x)
c) f(x) = f(π/2+x)
d) f(x) = f(π/2-x)
e) f(x) = f(2x)
f) f(x) = f(-x) =...
Homework Statement
A rectangular box measuring a x b x c has all its walls at temperature T1 except for the one at z=c which is held at temperature T2. When the box comes to equilibrium, the temperature function T(x,y,z) satisfies ∂T/∂t =D∇2T with the time derivative on the left equal to zero...
Homework Statement
Derive the expression for coefficients of Fourier series in exponential form for the sequence of rectangular pulses (with amplitude A, period T and duration θ) shown in this image:
Derive the expression for signal power depending on the coefficients of Fourier series...
Homework Statement
A violin string is plucked to the shape of a triangle with initial displacement:
y(x,0) = { 0.04x if 0 < x < L/4
(0.04/3)(L-x) if L/4 < x < L
Find the displacement of the string at later times. Plot your result up to the n = 10...
Q: Suppose ##u(x,t)## satisfies the heat equation for ##0<x<a## with the usual initial condition ##u(x,0)=f(x)##, and the temperature given to be a non-zero constant C on the surfaces ##x=0## and ##x=a##.
We have BCs ##u(0,t) = u(a,t) = C.## Our standard method for finding u doesn't work here...
Self Study
1. Homework Statement
Consider a periodic function f (x), with periodicity 2π,
Homework Equations
##A_{0} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)dx##
##A_{n} = \frac{2}{L}\int_{X_{o}}^{X_{o}+L}f(x)cos\frac{2\pi rx}{L}dx##
##B_{n} =...
Homework Statement
Find the values of the constant a for which the problem y''(t)+ay(t)=y(t+π), t∈ℝ, has a solution with period 2π
which is not identically zero. Also determine all such solutions
Homework Equations
With help of Fourier series I know that :
Cn(y''(t))= -n2*Cn(y(t))
Cn(y(t+π)) =...
< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown >
Hi all. I'm completely new to these forums so sorry if I'm doing anything wrong.
Anyway, I have this question...
Find the Fourier series for the periodic function
f(x) = x^2 (-pi < x < pi)...
Hi PH.
Let ##u_i(\mathbf{x},t)## be the velocity field in a periodic box of linear size ##2\pi##. The spectral representation of ##u_i(\mathbf{x},t)## is then
$$u_i(\mathbf{x},t) = \sum_{\mathbf{k}\in\mathbb{Z}^3}\hat{u}_i(\mathbf{k},t)e^{\iota k_jx_j}$$ where ι denotes the usual imaginary...
Homework Statement
Link: http://i.imgur.com/klFmtTH.png
Homework Equations
a_0=\frac{1}{T_0}\int ^{T_0}_{0}x(t)dt
a_n=\frac{2}{T_0}\int ^{\frac{T_0}{2}}_{\frac{-T_0}{2}}x(t)cos(n\omega t)dt
\omega =2\pi f=\frac{2\pi}{T_0}
The Attempt at a Solution
Firstly, x(t) is an even function because...
Hello, PF!
I am currently learning Fourier series (and then we'll move on to the Fourier transform) in one of my courses, and I'm having a hard time finding motivation for its uses. Or, in other words, I can't seem to find its usefulness yet. I know one of its uses is to solve the heat...
Homework Statement
let ##g## be a ##C^1## function such that the two series ##\sum_{-\infty}^{\infty} g(x+2n\pi)## and ##\sum_{n=-\infty}^{\infty} g'(x+2n\pi)## are uniformly convergent in the interval ##0\leq x \leq 2\pi ##. Show the Poisson summation formula:
##\sum_{n=-\infty}^{\infty}...
Homework Statement
By applying the Gram–Schmidt procedure to the list of monomials 1, x, x2, ..., show that the first three elements of an orthonormal basis for the space L2 (−∞, ∞) with weight function ##w(x) = \frac{1}{\sqrt{\pi}} e^{-x^2} ##
are ##e_0(x)=1## , ##e_1(x)= 2x## ,##e_2(x)=...
Does anyone know if it is possible to solve an equation of the type
u_x=(sin(x))*(u)
on a periodic domain using the fft.
I have tried methods using convolutions but have had no success
thanks in advance
Good afternoon people. Recently I started taking a course at my college about Fourier series but I got extremely confused. Here's what's going on. In school we were asigned to use the symmetry formulas to find the Fourier series of the following:
f\left ( t \right )=\begin{cases}
1 & \text{ if...
Homework Statement
I'm trying to calculate the Fourier Series for a periodic signal defined as:
y = x 0<x<2Π
y = 0 2Π≤x<3Π
Homework Equations
Fn = 1/T ∫T f(t)cos(kwοt + θk)[/B]
cn/2 + ∑k=1k=∞(cn)cos(kwοt+θk)
cn= 2|Fn|
θk=∠Fn
The Attempt at a Solution
I got Cn =...