Result of conjugate symmetry property of DFT

1. What is the conjugation property of DFT?
2. What is conjugate symmetry property?
3. What is the real part of conjugate symmetric signal?
4. Why is DFT symmetric?

What is the conjugation property of DFT?

Statement: The DFT of a complex conjugate of any sequence is equal to the complex conjugate of the DFT of that sequence; with the sequence delayed by k samples in the frequency domain.

What is conjugate symmetry property?

A function f(a) is conjugate symmetric if f∗(-a) = f(a). Definition. A function f(a) is conjugate antisymmetric if f∗(-a) = -f(a). If f(a) is real and conjugate symmetric, it is an even function. If f(a) is real and conjugate antisymmetric, it is an odd function.

What is the real part of conjugate symmetric signal?

Every real signal, therefore, consists of an equal contribution of positive and negative frequency components.

Why is DFT symmetric?

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.