How to choose between taking the real part or the absolute value of an inverse discrete Fourier transform?

1. What is difference between DFT and IDFT?
2. How is the FFT algorithm applied to determine inverse discrete Fourier transform?
3. What is phase factor or twiddle factor?

What is difference between DFT and IDFT?

The DFT allows one to convert a set of digital time samples to its frequency domain representation. In contrast, the IDFT can be used to invert the DFT samples, allowing one to reconstruct the signal samples x(k) directly from its frequency domain form, X(m).

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.

What is phase factor or twiddle factor?

A twiddle factor, in fast Fourier transform (FFT) algorithms, is any of the trigonometric constant coefficients that are multiplied by the data in the course of the algorithm. This term was apparently coined by Gentleman & Sande in 1966, and has since become widespread in thousands of papers of the FFT literature.