DFT problem help

1. What is the DFT formula?
2. What is DFT explain with example?
3. Why is DFT useful?

What is the DFT formula?

xn=N1k=0∑N−1Xke2πikn/N. The DFT is useful in many applications, including the simple signal spectral analysis outlined above.

What is DFT explain with example?

the DFT spectrum is periodic with period N (which is expected, since the DTFT spectrum is periodic as well, but with period 2π). Example: DFT of a rectangular pulse: x(n) = 1, 0 ≤ n ≤ (N − 1), 0, otherwise.

Why is DFT useful?

Chemists use DFT to calculate the approximate electronic structures of molecules or materials and thus predict their properties. The exact electronic structure of any system can be found by solving the Schrödinger equation, which mathematically describes a system's quantum mechanical wave function.