I want to know if a system has a linear phase response using frequency response of this system.
So I got phase response of it and also group delay.
and after that I got to know that if group delay is a constant for all ω, this system has a linear phase response.
so questions are
Group delay = $1/(1+\omega^2)$ . so $\omega=0$, group delay is $1$ and $\omega=1$ group delay is $1/2$. This is not a constant for all $\omega$ so I think this system has not a linear phase response. Is it correct?
when $H \left( e^{j\omega} \right)$ = $-e^{-j\omega} + 2 e^{-2j\omega} - e^{-3j\omega}$. Can I also know if this system has a linear phase response with same logic in question 1?