Need help to find application of the Fourier series and Fourier Transforms

Click For Summary

Homework Help Overview

The original poster seeks to identify various applications of Fourier series and Fourier transforms as part of a school task. The discussion revolves around the relevance of these mathematical tools in different fields.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants mention specific applications such as mp3 encoding, heat diffusion, and their roles in electronics and quantum mechanics. There are references to their use in solving partial differential equations and approximating functions through truncated Fourier series. Additionally, a historical application by Lord Kelvin is noted, prompting further inquiry into the method used.

Discussion Status

The discussion is active, with participants contributing various examples and applications. Some participants express interest in further details about specific applications, indicating a collaborative exploration of the topic.

Contextual Notes

No specific constraints or imposed homework rules are mentioned, but the focus remains on gathering applications rather than solving a particular problem.

paul-martin
Messages
27
Reaction score
0
Hi, i got a task in school, in which I shall find as many application of the Fourier series And Fourier Transforms as possible. Any suggestion?

Kindly Paul-Martin
 
Physics news on Phys.org
mp3 encoding is 1 example of Fourier transform
 
heat diffusion is the reason why Fourier came up with the Fourier series in the first place! :biggrin:


lots of applications in electronics.

fourier transform is used in quantum mechanics.

also, Fourier series come up in solutions to partial differential equations like the wave equation, laplace's equation, diffusion equation, etc.
 
Intresting
 
From a Linear Algebra standpoint, truncated Fourier series are the best approximation to a function over an interval. (from a subspace defined by basis vectors sinx,cosx,...sin(nx),cos(mx).
So take the first few terms, and you have a good approximation.
 
K thank you!

Any more suggestions?
 
Lord Kelvin use Fourier transforms to calculate the age of the earth. :smile:
 
quasar987 said:
Lord Kelvin use Fourier transforms to calculate the age of the earth. :smile:

Really, could you tell me how he did that?
 
when you want to obtain the response of a system to a input while you have the response to a sine function you could expand input function using Fourier series and by superposition law obtain the response to the input function.
 

Similar threads

Analysis Need Self study book for Fourier Series and Generalized Functions
  • · Replies 7 ·
Replies
7
Views
467
A few questions to make sure I understand Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad The precise relationship between Fourier series and Fourier transform
  • · Replies 12 ·
Replies
12
Views
4K
Graduate Polar Fourier transform of derivatives
  • · Replies 4 ·
Replies
4
Views
3K
Fourier/heat problem involving hyperbolic sine
  • · Replies 3 ·
Replies
3
Views
1K
Fourier transform of single pulse & sequence of pulses
  • · Replies 5 ·
Replies
5
Views
5K
Quantum Mechanics I, finding impuls wavefunction.
  • · Replies 6 ·
Replies
6
Views
1K
Solve integral by finding Fourier series of complex function
  • · Replies 3 ·
Replies
3
Views
2K
How to calculate freezing time for a moist food by-product (75% water)
  • · Replies 6 ·
Replies
6
Views
1K
Fourier transform radial component of magnetic field
  • · Replies 5 ·
Replies
5
Views
2K