$($Difficulty: $*****)$ Choose the correct statements from the choices below.

Consider the length $N$ signal $x[n]=cos(\frac{2}{N}Ln+),$ where $N$ is even and $L=\frac{N}{2}.$ Then $x[k]=\{\begin{array}{ccc}\frac{N}{2}{e}^j& \text{f}\text{o}\text{r}& k=L\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}.$

If we apply the DFT twice to a signal $x[n],$ we obtain the signal itself scaled by $N,$ i$.$e$.N_x[n].$

Consider the length $-N$ signal $x[n]=(-1{)}^n$ with $N$ even. Then $x[k]=0$ for all $k$ except $k=\frac{N}{2}$