Non-symmetrical DFT of real valued signal

1. Is DFT symmetrical?
2. Why is the DFT mirrored?
3. What is real DFT?
4. How do you calculate DFT coefficient?

Is DFT symmetrical?

And without going into mathematical details, DFT of real valued function is symmetric, i.e. resultant Fourier function has both real and imaginary parts which are mirror images with respect to 0 frequency component.

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.

What is real DFT?

The real discrete Fourier transform (RDFT) corresponds to the Fourier series for sampled periodic signals with sampled periodic frequency responses just as discrete Fourier transform (DFT) corresponds to the complex Fourier series for the same type of signals.

How do you calculate DFT coefficient?

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 ) .