Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The Fourier Transform

  1. Aug 22, 2006 #1
    Hello everyone ^^

    Why I can say "The Fourier transform tells us " how much sinusoid" there is in the waveform at a given frequency "w""

    Form Linear circuit analysis by Artice M. David

    thanks a lot
     
  2. jcsd
  3. Aug 22, 2006 #2

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It is meant in the following sense...

    if you take the Fourier transform of a function F(x), the result is a function A(w), right?

    [tex]\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}F(x)e^{-iwx}dx=A(w)[/tex]

    Well it turns out that this function A(w) is such that

    [tex]F(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}A(w)e^{iwx}dw[/tex]

    i.e. A(w) is the amplitude of the sine wave [itex]e^{iwx}[/itex] of frequency w. So the bigger A is for a given w, the bigger the contribution of this sine wave in the integral making up F(x).

    You must think in terms of analogy with Fourier series.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: The Fourier Transform
  1. Fourier Transform (Replies: 2)

  2. Fourier transform? (Replies: 3)

  3. Fourier Transformations (Replies: 10)

Loading...