From a discrete$-$time signal $x(n)$ with Fourier transform $x(),$ shown in determine and sketch the Fourier transform of the following signals:

a$.y_1(n)=\{\begin{array}{ccc}x(n),& n\text{e}\text{v}\text{e}\text{n}& \\ 0,& n\text{o}\text{d}\text{d}& \end{array}$

b$.y_2(n)=x(2n)$

c$.y_3(n)=\{\begin{array}{ccc}x(\frac{n}{2}),& n\text{e}\text{v}\text{e}\text{n}& \\ 0,& n\text{o}\text{d}\text{d}& \end{array}$

Note that $y_1(n)=x(n)s(n),$ where $s(n)=\{dots,0,1,0,1,0,1,0,1,$dots$\}$