Calculate the $N$-point uniform sampling values of the Fourier transform of the following signal over $\left[ 0, 2 \pi\right]$ is (). $\operatorname{cos}\left(\frac{18 \pi n}{7}\right) + \operatorname{sin}(2n)$.

Options:
A. $$
\begin{array} {c} {{{{X ( k )=R_{1} ( k )+R_{2} ( k )=R_{1} ( \mathrm{e}^{j\pi_{k}} )+R_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{9 \pi} {N} k-\frac{2 2 \pi} {9}+6 \pi\Big)+\delta\Big( \frac{9 \pi} {N} k+\frac{2 2 \pi} {9}-1 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{9 \pi} {N} k-4 \Big)+\mathrm{i} \delta\Big( \frac{9 \pi} {N} k+4-2 \pi\Big) \Big\}}}} \\ \end{array}
$$
B. $$
\begin{array} {c} {{{{X ( k )=U_{1} ( k )+U_{2} ( k )=U_{1} ( \mathrm{e}^{j\pi_{k}} )+U_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{6 \pi} {N} k-\frac{2 1 \pi} {7}+1 \pi\Big)+\delta\Big( \frac{6 \pi} {N} k+\frac{2 1 \pi} {7}-8 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{6 \pi} {N} k-2 \Big)+\mathrm{i} \delta\Big( \frac{6 \pi} {N} k+2-1 \pi\Big) \Big\}}}} \\ \end{array}
$$
C. $$
\begin{array} {c} {{{{X ( k )=X_{1} ( k )+X_{2} ( k )=X_{1} ( \mathrm{e}^{j\pi_{k}} )+X_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{2 \pi} {N} k-\frac{1 8 \pi} {7}+2 \pi\Big)+\delta\Big( \frac{2 \pi} {N} k+\frac{1 8 \pi} {7}-4 \pi\Big)-}}} \\ {{{\mathrm{j} \delta\Big( \frac{2 \pi} {N} k-2 \Big)+\mathrm{j} \delta\Big( \frac{2 \pi} {N} k+2-2 \pi\Big) \Big\}}}} \\ \end{array}
$$
D. $$
\begin{array} {c} {{{{X ( k )=V_{1} ( k )+V_{2} ( k )=V_{1} ( \mathrm{e}^{j\pi_{k}} )+V_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{1 \pi} {N} k-\frac{1 0 \pi} {8}+6 \pi\Big)+\delta\Big( \frac{1 \pi} {N} k+\frac{1 0 \pi} {8}-7 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{1 \pi} {N} k-2 \Big)+\mathrm{i} \delta\Big( \frac{1 \pi} {N} k+2-4 \pi\Big) \Big\}}}} \\ \end{array}
$$
E. $$
\begin{array} {c} {{{{X ( k )=S_{1} ( k )+S_{2} ( k )=S_{1} ( \mathrm{e}^{j\pi_{k}} )+S_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{8 \pi} {N} k-\frac{1 6 \pi} {6}+5 \pi\Big)+\delta\Big( \frac{8 \pi} {N} k+\frac{1 6 \pi} {6}-4 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{8 \pi} {N} k-1 \Big)+\mathrm{i} \delta\Big( \frac{8 \pi} {N} k+1-3 \pi\Big) \Big\}}}} \\ \end{array}
$$
F. $$
\begin{array} {c} {{{{X ( k )=Z_{1} ( k )+Z_{2} ( k )=Z_{1} ( \mathrm{e}^{j\pi_{k}} )+Z_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{4 \pi} {N} k-\frac{2 0 \pi} {7}+1 \pi\Big)+\delta\Big( \frac{4 \pi} {N} k+\frac{2 0 \pi} {7}-3 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{4 \pi} {N} k-4 \Big)+\mathrm{i} \delta\Big( \frac{4 \pi} {N} k+4-2 \pi\Big) \Big\}}}} \\ \end{array}
$$
G. $$
\begin{array} {c} {{{{X ( k )=Y_{1} ( k )+Y_{2} ( k )=Y_{1} ( \mathrm{e}^{j\pi_{k}} )+Y_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{3 \pi} {N} k-\frac{1 5 \pi} {5}+3 \pi\Big)+\delta\Big( \frac{3 \pi} {N} k+\frac{1 5 \pi} {5}-6 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{3 \pi} {N} k-5 \Big)+\mathrm{i} \delta\Big( \frac{3 \pi} {N} k+5-3 \pi\Big) \Big\}}}} \\ \end{array}
$$
H. $$
\begin{array} {c} {{{{X ( k )=W_{1} ( k )+W_{2} ( k )=W_{1} ( \mathrm{e}^{j\pi_{k}} )+W_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{5 \pi} {N} k-\frac{1 9 \pi} {7}+4 \pi\Big)+\delta\Big( \frac{5 \pi} {N} k+\frac{1 9 \pi} {7}-5 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{5 \pi} {N} k-1 \Big)+\mathrm{i} \delta\Big( \frac{5 \pi} {N} k+1-1 \pi\Big) \Big\}}}} \\ \end{array}
$$
I. $$
\begin{array} {c} {{{{X ( k )=Q_{1} ( k )+Q_{2} ( k )=Q_{1} ( \mathrm{e}^{j\pi_{k}} )+Q_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{1 0 \pi} {N} k-\frac{2 3 \pi} {5}+4 \pi\Big)+\delta\Big( \frac{1 0 \pi} {N} k+\frac{2 3 \pi} {5}-2 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{1 0 \pi} {N} k-1 \Big)+\mathrm{i} \delta\Big( \frac{1 0 \pi} {N} k+1-5 \pi\Big) \Big\}}}} \\ \end{array}
$$
J. $$
\begin{array} {c} {{{{X ( k )=T_{1} ( k )+T_{2} ( k )=T_{1} ( \mathrm{e}^{j\pi_{k}} )+T_{2} ( \mathrm{e}^{j \pi_{k}} )}}}} \\ {{{=\pi\Big\{\delta\Big( \frac{7 \pi} {N} k-\frac{1 7 \pi} {8}+2 \pi\Big)+\delta\Big( \frac{7 \pi} {N} k+\frac{1 7 \pi} {8}-3 \pi\Big)-}}} \\ {{{\mathrm{i} \delta\Big( \frac{7 \pi} {N} k-3 \Big)+\mathrm{i} \delta\Big( \frac{7 \pi} {N} k+3-2 \pi\Big) \Big\}}}} \\ \end{array}
$$
Answer: C