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Suppose I have a fourier transform $X(f)$ of an energy signal $x(t)$. Now how do I interpret that continuous fourier transform plot. For example if the input signal is a rectangular pulse the fourier tansform is Sinc function. How do I interpret this continuous fourier transform plot?

Here is my understanding: In the case of fourier series, the plot consists of disrete values. Each discrete spike implies a sinusoid at particular frequency. Can we extend the same notion to the CTFT. ie infinitesimally close spikes which implies particular sinusoids at particular frequencies.

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    $\begingroup$ Essentially, to synthesize the original signal from the Fourier transform you do the same thing as with Fourier series, replacing summations with integrals. $\endgroup$ – dls Oct 2 '13 at 6:43
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    $\begingroup$ Think of discrete vs. continuous random variables. A discrete r.v. is described by discrete values (probabilities). A continuous r.v. is described by probability density function. Similarly, the Fourier series lists particular frequences, while the Fourier transform is the frequency density function. $\endgroup$ – user98130 Oct 3 '13 at 3:10
  • $\begingroup$ @user98130 : Yes Now I am getting some idea of these infinitesimals. One of my other doubts recently was closer to the same idea. math.stackexchange.com/questions/512125/… $\endgroup$ – dexterdev Oct 3 '13 at 3:58

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