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At first, I give the definition of the inverse discrete-time Fourier transform

$$\phi(s)=\frac{1}{2\pi}\int_{-\pi}^{\pi}\exp(iks)f(k)dk$$

Here what I use is

ResourceFunction["NInverseFourierSequenceTransform"][GGG[k, t], k, 1]

It seems that for some complex functions, the above command is very slow.

Are there some programs which are faster than the 'NInverseFourierSequenceTransform'?

Any suggestion is welcome!

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    $\begingroup$ The function I used is very complex which needs more time to compute. $\endgroup$
    – Blueka
    Jul 14 '20 at 20:33
  • $\begingroup$ Have you looked at FourierTransform and its inverse? $\endgroup$
    – bill s
    Jul 15 '20 at 3:24
  • $\begingroup$ @bills The upper and the bottom limits of the integral of the InverseFourierTransform are different from the inverse discrete-time Fourier transform. $\endgroup$
    – Blueka
    Jul 15 '20 at 5:25
  • $\begingroup$ If you're assuming periodicity, then how about FourierSinCoefficient and/or FourierCosCoefficient, or FourierSinSeries and/or FourierCosSeries? $\endgroup$
    – bill s
    Jul 15 '20 at 13:02

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