# Is there some programs about the fast inverse descrete time Fourier transform

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!

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