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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.

dexterdev
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    Essentially, to synthesize the original signal from the Fourier transform you do the same thing as with Fourier series, replacing summations with integrals. – dls Oct 02 '13 at 06:43
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    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. – user98130 Oct 03 '13 at 03:10
  • @user98130 : Yes Now I am getting some idea of these infinitesimals. One of my other doubts recently was closer to the same idea. http://math.stackexchange.com/questions/512125/what-is-the-probability-of-a-continuous-uniform-random-variable-in-0-1-to-be?noredirect=1#comment1098034_512125 – dexterdev Oct 03 '13 at 03:58

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