What is the DFT of DFT of discrete signal [duplicate]

1. What happens if we apply DFT twice to a signal?
2. What is the relation between DCT and DFT?
3. How is DFT calculated?
4. What do you mean by DFT Discrete Fourier Transform discuss the difference of it with DCT discrete cosine transform?

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.

What is the relation between DCT and DFT?

DCT is similar to the Discrete Fourier Transform (DFT), but using only real numbers. DCT are equivalent of DFT of roughly twice the length, operating on real data with even symmetry and in some variants the input or output data are shifted by half a sample.

How is DFT calculated?

The DFT formula for X k X_k Xk​ is simply that X k = x ⋅ v k , X_k = x \cdot v_k, Xk​=x⋅vk​, where x x x is the vector ( x 0 , x 1 , … , x N − 1 ) .

What do you mean by DFT Discrete Fourier Transform discuss the difference of it with DCT discrete cosine transform?

Like the discrete Fourier transform (DFT), a DCT operates on a function at a finite number of discrete data points. The obvious distinction between a DCT and a DFT is that the former uses only cosine functions, while the latter uses both cosines and sines (in the form of complex exponentials).