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Fourier Transformations

  1. Mar 5, 2009 #1
    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
     
  2. jcsd
  3. Mar 5, 2009 #2

    mathman

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    Try wikipedia. It can't be explained in a few sentences.
     
  4. Mar 5, 2009 #3
    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.
     
  5. Mar 5, 2009 #4
    how old are you? what level mathematical maturity do you have?
     
  6. Mar 5, 2009 #5
    Not really sure why it matters but im 21. hmmm not that much i guess?
     
  7. Mar 5, 2009 #6
    you know anything about vectors? how you can express any vector as a sum of basis vectors?
     
  8. Mar 5, 2009 #7
    hmmm cant say that I do, is that where I should start then?
     
  9. Mar 5, 2009 #8
    what do you know then? why do you want to know about fourier transforms?
     
  10. Mar 6, 2009 #9
    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.
     
    Last edited by a moderator: May 4, 2017
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