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Suppose we have a continuous and periodic real-valued 1D signal $f(t)$. Let us say we obtain finite number of samples $f(n)$ from $f(t)$. Is there a way to take discrete Fourier transform of $f(n)$ and obtain data similar to $F(\omega)$, Fourier transform of $f(t)$? If this is possible, how do we convert discrete Fourier transformed frequency data into time format?

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  • $\begingroup$ Well, to get the DFT you really just calculate it. Usually one would use the FFT algorithm for efficiency, but you don't have to. As for going back to the time domain, you likewise simply calculate the inverse DFT. I don't know how else to read your question. $\endgroup$ Commented Mar 5, 2015 at 0:19
  • $\begingroup$ This answer to a related question should be helpful. $\endgroup$
    – Matt L.
    Commented Mar 5, 2015 at 13:44

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If the samples are equally spaced then the Fourier Transform coefficients $F(\omega)$ are the Discrete Fourier Transform coefficients.

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