Applications of Fourier series and Fourier transforms

[paul-martin]

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

 

[hanhao]

mp3 encoding is 1 example of Fourier transform

 

[Brad Barker]

heat diffusion is the reason why Fourier came up with the Fourier series in the first place!


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.

 

[paul-martin]

Intresting

 

[shaner-baner]

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.

 

[paul-martin]

K thank you!

Any more suggestions?

 

[quasar987]

Lord Kelvin use Fourier transforms to calculate the age of the earth.

 

[n.karthick]

Lord Kelvin use Fourier transforms to calculate the age of the earth.

Really, could you tell me how he did that?

 

[rezaborhani]

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.