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

In summary, The Fourier series and Fourier transforms have numerous applications in various fields such as mp3 encoding, heat diffusion, electronics, quantum mechanics, and solutions to partial differential equations. They are also useful in approximating functions and have been used by Lord Kelvin to calculate the age of the earth. Additionally, they can be used to obtain the response of a system to a given input function using the superposition law.
  • #1
paul-martin
27
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
 
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  • #2
mp3 encoding is 1 example of Fourier transform
 
  • #3
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.
 
  • #4
Intresting
 
  • #5
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.
 
  • #6
K thank you!

Any more suggestions?
 
  • #7
Lord Kelvin use Fourier transforms to calculate the age of the earth. :rofl:
 
  • #8
quasar987 said:
Lord Kelvin use Fourier transforms to calculate the age of the earth. :rofl:

Really, could you tell me how he did that?
 
  • #9
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.
 

1. What are Fourier series and Fourier Transforms?

Fourier series and Fourier Transforms are mathematical tools used to analyze and decompose a complex signal into its individual frequency components. They are commonly used in signal processing, image and sound analysis, and other fields of science and engineering.

2. How are Fourier series and Fourier Transforms applied in science?

Fourier series and Fourier Transforms have many applications in science, including in the analysis of electrical signals, gravitational waves, and quantum mechanics. They are also used in image and sound processing, such as removing noise from images or enhancing sound quality.

3. What is the difference between Fourier series and Fourier Transforms?

Fourier series are used for periodic signals, while Fourier Transforms are used for non-periodic signals. Fourier series breaks down a periodic signal into its individual frequency components, while Fourier Transforms analyze the entire frequency spectrum of a non-periodic signal.

4. Can Fourier series and Fourier Transforms be used in real-world applications?

Yes, Fourier series and Fourier Transforms are widely used in various real-world applications, such as in engineering, telecommunications, and medical imaging. They are powerful tools for analyzing and processing signals and have greatly contributed to technological advancements in these fields.

5. Are there any limitations to using Fourier series and Fourier Transforms?

While Fourier series and Fourier Transforms are powerful tools, they do have limitations. For example, they assume that signals are infinite and continuous, which may not always be the case in real-world applications. Additionally, they may not be suitable for analyzing signals with sudden changes or discontinuities.

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