Problem $2$: $[48$pts$]$ Compute the CT Fourier transform of the following signals.

a$)x(t)=e^{-t}cos({}_{0}t)u(t),>0,$

c$)(\frac{sin(t)}{t})(\frac{sin(2(t-1))}{(t-1)})$

b$)x(t)=\{\begin{array}{ccc}1+cos(t)& if& |t|1\\ 0& \text{e}\text{l}\text{s}\text{e}& \end{array}$

e$)x_0(t)=\{\begin{array}{ccc}{e}^{-t}& if& 0t1\\ 0& \text{e}\text{l}\text{s}\text{e}& \end{array}$

d$)x(t)$ shown in left side of Fig. $1.$

f$)x_2(t)$ shown in right side of Fig. $1.$

Figure $1$: Signals for Problem $2.$ In the right signal, $x_0(t)$ refers to the signals defined in part e$).$