Fourier Series of Periodic Function

Click For Summary

Homework Help Overview

The discussion revolves around finding the Fourier coefficients for a periodic function and estimating the series for specific values of n (4, 20, and 100). The context involves understanding the properties of Fourier series and their application to a function that exhibits discontinuities.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the Fourier coefficients and expresses uncertainty about the correctness of their results, particularly regarding the discontinuities in the function. Other participants discuss the computation of the a0 coefficient and suggest potential corrections to the original poster's approach.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's calculations and confirming the method's validity. There is a focus on ensuring the mathematical accuracy of the coefficients, particularly a0, but no consensus has been reached on the final results.

Contextual Notes

Participants are working with a function that is discontinuous at certain points, which may affect the Fourier series representation. There is also mention of discrepancies in the coefficients derived from different methods, such as using Mathematica.

he1senberg
Messages
4
Reaction score
0

Homework Statement


http://imageshack.us/photo/my-images/824/50177563.png/
I need to find the Fourier coefficients and estimate the series for certain values of n. (4, 20 and 100)


Homework Equations


http://imageshack.us/photo/my-images/839/32591148.png/



The Attempt at a Solution


I was unsure about what to do and found the equation above. So I used it and b coefficient was 0. I set the period 2L as 3, and set -L -3/2 and L as 3/2. So the total value I found was
a0 + Σ(3/(n*pi) - 27/(2*(n*n*n)*(pi*pi*pi)))*sin(2*n*pi/3)+ 9*cos(2*n*pi/3)/(2*(n*n)*(pi*pi))*(cos(2n*pi*x/3)

I managed to get some result but I am not sure if my results are correct, as the graph of the function is discontinuous at the ends of parabola. So, do you think my answer is correct? If not, how can I fix it?
 
Physics news on Phys.org
I have Mathematica crank out the integral, and it produced almost the same result. The only difference is that there shouldn't be 2 in the denominator of the last term.

What did you get for a0?
 
Thanks for reply.

I think a0 was 2/9 or 4/9, I don't have the paper with me right now. I think that last 2 should be 4. Other than that, do you think my procedure to deal with problem is correct? Because I couldn't really make sure that I solved the problem correctly.
 
Yes, your method sounds fine. It's just getting the math right now. a0 is the average value of the function over one period, so it should be 2/9.
 

Similar threads

Minimizing the energy required to break a cylinder of fluid into droplets
  • · Replies 9 ·
Replies
9
Views
3K
Quantum Well Centred at the Origin Doubled in Size at time t=0. Symmetry seems to render the question incorrect
  • · Replies 4 ·
Replies
4
Views
2K
Discrepancies In Clebsch–Gordan Calculations (Dipole Transitions)
  • · Replies 0 ·
Replies
0
Views
1K
Particle in a box that suddenly expands
  • · Replies 15 ·
Replies
15
Views
4K
Most Probable energy after infinite square well expands
  • · Replies 2 ·
Replies
2
Views
3K
Wave Function for a Particle in a Symmetric Infinite Square Well
  • · Replies 7 ·
Replies
7
Views
2K
Derive and Solve the Lane-Emden Equation for a Polytropic Gas Sphere
  • · Replies 6 ·
Replies
6
Views
3K
A few questions to make sure I understand Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
Relationship between Fourier coefficients and power spectral density
  • · Replies 1 ·
Replies
1
Views
2K
Dirac Delta using periodic functions
  • · Replies 3 ·
Replies
3
Views
3K