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What is fourier series/fourier transform?

  1. Sep 21, 2011 #1
    can anyone give me a simple explanation what fourier analysis is all about? i have read wiki and it is a little confusing

    what am i doing when i express a funciton as a series? what is the difference to a transform?

    i know how to follow the steps of a fourier series/transform, but i have no idea why i am doing it?

    thanks!
     
  2. jcsd
  3. Sep 21, 2011 #2
    assuming i have a function f(x) = x

    what does it mean to take the fourier series?

    what does it mean to take hte fourier transform?
     
  4. Sep 21, 2011 #3

    mathman

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  5. Sep 22, 2011 #4
    is fourier series something like taylor expansion? where greater powers of the terms give better accuracy of the particular function?
     
  6. Sep 22, 2011 #5
    i refer you to the section "introduction" , where at the end of this section, they described the fourier transform as decomposing an oscillating function into several sines and cosines.

    if i understood correctly what the 4 graphs are saying, does it mean that when i fourier transform the first graph (blue), i will get a transformed that is (green, when i sub 3 hz into the fourier transformed expression) and (red when i sub in 5hz into the fourier transformed expression)

    and when i integrate these 2 expressions, i will get 0.5(green) and 0.000.... (red)

    so the value 0.5 and 0.0000... is akin to telling me the fraction of blue graph that oscillates at 3 hz is 0.5, while the fraction of blue graph that oscillates at 5hz is 0.0000...?

    is this what fourier transform is about?

    thanks!
     
  7. Sep 22, 2011 #6
    A Fourier Series approximation of a periodic waveform = a sum of sines and cosines of varying amplitudes of multiples of the the fundamental frequency of that waveform. FS is a discrete series approximation.

    A Fourier Transform essentially converts a time domain function to its frequency domain components. That is its spectral content. For example the FT of a sine wave would just be a single spike at the given frequency. If the sine wave has harmonics, as in a guitar or piano tone, then the FT would be a series of spikes; one each at the fundamental frequency and 3rd and 5th and 7th etc all with declining amplitudes.
    FT is a continuous function approximation.
     
    Last edited: Sep 22, 2011
  8. Sep 22, 2011 #7
    oh..

    so when i integrate over all frequency, does it have to = 1?
     
  9. Sep 22, 2011 #8
    No, you are thinking of Probability Density functions. The area under that curve =1

    For spectral content, the ENERGY of the spectra must equal the energy calculated from the time domain waveform.
     
  10. Sep 23, 2011 #9
    this is confusing

    thanks!
     
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