DFT product of sinusoids

1. What does DFT output?
2. How is DFT calculated?
3. Is output of DFT periodic?
4. What is the difference between DFT and DTFS?

What does DFT output?

All DFT outputs for a real N-sample input sequence with even N follow this pattern: 1 real value, N/2-1 complex values, 1 real value, N/2-1 conjugates. A diagram of the 64-point example is shown below, where blue squares indicate non-redundant information.

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 ) .

Is output of DFT periodic?

the DFT spectrum is periodic with period N (which is expected, since the DTFT spectrum is periodic as well, but with period 2π).

What is the difference between DFT and DTFS?

DFT (Discrete Fourier Transform) is a practical version of the DTFT, that is computed for a finite-length discrete signal. The DFT becomes equal to the DTFT as the length of the sample becomes infinite and the DTFT converges to the continuous Fourier transform in the limit of the sampling frequency going to infinity.