Calculation number and meaning of DFT

1. How is DFT calculated?
2. Why DFT is calculated?
3. What does N point DFT mean?
4. What are DFT coefficients?

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 ) .

Why DFT is calculated?

The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware.

What does N point DFT mean?

Definition. An N-point DFT is expressed as the multiplication , where is the original input signal, is the N-by-N square DFT matrix, and. is the DFT of the signal.

What are DFT coefficients?

DFT coefficients, Xk, give amplitudes and phases of complex sinusoids at integer frequencies k, from 0 to N−1, that sum to the original signal x[n], comprised of N points.