Inverse DFT on the first half time domain

1. Is DFT periodic in time domain?
2. What is an N point DFT?
3. How is the FFT algorithm applied to determine inverse discrete Fourier transform?

Is DFT periodic in time domain?

the DFT spectrum is periodic with period N (which is expected, since the DTFT spectrum is periodic as well, but with period 2π).

What is an N point DFT?

Definition. An N-point DFT is expressed as the multiplication , where is the original input signal, is the N-by-N square DFT matrix, and. is the DFT of the signal.

How is the FFT algorithm applied to determine inverse discrete Fourier transform?

In the IDFT formula, we have two different multiplying factors. Thus if we multiply with a factor of 1/N and replace the twiddle factor with its complex conjugate in the DIF algorithm's butterfly structure, we can get the IDFT using the same method as the one we used to calculate FFT.