1. ### I Fourier Series and Cepheid Variables

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...
2. ### Analysis Books for learning Fourier series expansion

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...
3. ### Finding the fourier spectrum of a function

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 =...
4. ### Find the Fourier Series of the function

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 +...
5. ### Fourier Series Expansion

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...

8. ### Derivation of the Fourier series of a real signal

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...
9. ### Using Maxima to plot error in Fourier 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...
10. ### Insights Further Sums Found Through Fourier Series - Comments

Svein submitted a new PF Insights post Further Sums Found Through Fourier Series Continue reading the Original PF Insights Post.
11. M

### Fourier Series of a function not centered at zero

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...
12. ### Find Fourier coefficients - M. Chester text

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...
13. ### Fourier Series of Sawtooth Wave from Inverse FT

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...
14. ### Fourier Series Coefficient Symmetries

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) =...
15. ### Fourier/heat problem involving hyperbolic sine

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...
16. ### Evaluate Fourier series coefficients and power of a signal

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...
17. ### Fourier Series/Wave Problem

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...
18. ### Change of variables in Heat Equation (and Fourier Series)

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...
19. ### Fourier Series Problem

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} =...
20. ### Fourier series and differential equations

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)) =...
21. ### Insights Using the Fourier Series To Find Some Interesting Sums - Comments

Svein submitted a new PF Insights post Using the Fourier Series To Find Some Interesting Sums Continue reading the Original PF Insights Post.
22. ### Find the Fourier series for the periodic function

< 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)...
23. ### I Spectral representation of an incompressible flow

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...
24. ### Fourier Series Coefficients of an Even Square Wave

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...
25. ### I Motivation for Fourier series/transform

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...
26. ### Poisson summation formula

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}...
27. ### Generalised Fourier Series

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)=...
28. ### I Solving u_x=(sin(x))*(u) in Fourier space

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