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A signal $x(n)=\sin \left(\omega_{0} n+\phi\right)$ is the input to a linear time-invariant system having a frequency response $\text{H}(e^{j \omega})$. If the output of the system $A x\left(n-n_{0}\right)$, then the most general form of $\angle \mathrm{H}\left(\mathrm{e}^{j \omega}\right)$ will be

1. $-n_{0} \omega_{0}+\beta$ for any arbitrary real $\beta$.
2. $-n_{0} \omega_{0}+2 \pi k$ for any arbitrary integer $k$.
3. $n_{0} \omega_{0}+2 \pi k$ for any arbitrary integer $k$.
4. $-n_{0} \omega_{0} \phi$.