Different results applying DFT (formula only) and FFT on Matlab?

1. What is the advantage of FFT instead of direct computation of DFT?
2. What happens if we apply DFT twice to a signal?
3. What is the difference between the DFT and FFT of a signal?

What is the advantage of FFT instead of direct computation of DFT?

FFT helps in converting the time domain in frequency domain which makes the calculations easier as we always deal with various frequency bands in communication system another very big advantage is that it can convert the discrete data into a contionousdata type available at various frequencies.

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 difference between the DFT and FFT of a signal?

Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its representation in the frequency domain. Whereas, Fast Fourier Transform (FFT) is any efficient algorithm for calculating the DFT.