How to make DFT in matlab without FFT [duplicate]

1. Is DFT and FFT same?
2. What happens if we apply DFT twice to a signal?
3. What makes FFT efficient compared to DFT?
4. Why is the DFT mirrored?

Is DFT and FFT same?

It is important to note that while computationally dif- ferent, the FFT algorithm is functionally equivalent to the DFT; it simply achieves computational savings by exploiting symmetries in the definition of the DFT.

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 makes FFT efficient compared to DFT?

The key to the power of the fast Fourier transform (FFT), as compared to the discrete Fourier transform (DFT), is the bit reversal scheme of the Cooley-Tukey algorithm [1].

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.