Confusion related to DFT in a paper [closed]

1. What are the disadvantages of direct computation of DFT?
2. What happens if we apply DFT twice to a signal?
3. Can DFT be complex?
4. Why is the DFT mirrored?

What are the disadvantages of direct computation of DFT?

For the computation of N-point DFT, N2 complex multiplications and N[N-1] Complex additions are required. If the value of N is large than the number of into lakhs. This proves inefficiency of direct DFT computation.

What happens if we apply DFT twice to a signal?

Applying the DFT twice results in a scaled, time reversed version of the original series. The transform of a constant function is a DC value only.

Can DFT be complex?

However, the complex DFT projects the input signal on exponential basis functions (Euler's formula connects these two concepts). When the input signal in the time domain is real valued, the complex DFT zero-fills the imaginary part during computation (That's its flexibility and avoids the caveat needed for real DFT).

Why is the DFT mirrored?

Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way.