Fourier Transformations

  • Thread starter skaboy607
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  • #1
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Can anyone explain the above-i've read about in books, internet sites and still do not understand what its doing or the maths.

Thanks
 

Answers and Replies

  • #2
mathman
Science Advisor
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Try wikipedia. It can't be explained in a few sentences.
 
  • #3
108
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hmm, ive read that and although i understand the basic, i.e complicated function and representing with smaller functions with sin and cosine waves, the rest doesn't make sense no matter how many times I read it.
 
  • #4
1,707
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how old are you? what level mathematical maturity do you have?
 
  • #5
108
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Not really sure why it matters but im 21. hmmm not that much i guess?
 
  • #6
1,707
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you know anything about vectors? how you can express any vector as a sum of basis vectors?
 
  • #7
108
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hmmm cant say that I do, is that where I should start then?
 
  • #8
1,707
5
what do you know then? why do you want to know about fourier transforms?
 
  • #9
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An intuitive explanation:
I am sure you have seen one of these http://en.wikipedia.org/wiki/Spectral_analyzer" [Broken] found on Hi-Fi's or digital audio players, that plot frequency vs. amplitude. They take the audio signal (amplitude/time), apply the (discrete) Fourier transform, and display the resulting function (amplitude/frequency).

To illustrate, take the function [tex]\cos(2\pi at)[/tex], which is a wave with frequency [tex]a[/tex]. Its Fourier transform is zero except for two "spikes" at [tex]-a[/tex] and [tex]a[/tex].


A more mathematical reason why the Fourier transform is important, is that it turns differentiation into multiplication, see http://en.wikipedia.org/wiki/Fourier_Transform#Analysis_of_differential_equations", which is quite useful for solving some differential equations.
 
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