The Fourier Transform

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
 

quasar987

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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.
 

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