If $x(n)$ is a [[finite-duration discrete-time signal]] of real values, the coefficients of its DFT, $X(k)$ is an even sequence, that is, they have the following property: $ |X(k)| = |X(N-k)|, \ 0 \le k \le N-1 $ and $ \angle X(k) = - \angle X(N-k), \ 0 \le k \le N-1 $ For this reason, for real signals, we can limit the range of the spectrum to half of the sampling frequency without loss of information.