Ideal Delay

$x[n] = \delta[n-5] = \begin{cases} 1, & n=5, \\ 0, & n\neq 5\end{cases} \\ X(f) = e^{-j2\pi f 5}$

time domain

frequency domain - real and imaginary parts

Note: $x[n]$ is real and $X(f)$ has Hermitian symmetry ( $\Re\{X(f)\}$ is even and $\Im\{X(f)\}$ is odd).

magnitude frequency response

Note: $x[n]$ is real and $|X(f)|$ is even.

log magnitude frequency response

wrapped phase response

Note: x[n] is real and $\angle X(f)$ is odd.

unwrapped phase response