(a) (21 points) Find the Fourier transform of each of the signals given below:Hint: you may use Fourier Transforms derived in class. \text { i. (optional) } x_{1}(t)=2 \text {

rect }\left(\frac{-t-3}{2}\right) \cos (10 \pi t) \text { ii. } x_{2}(t)=e^{(2+3 j) t} u(-t+1) \text { iii. } x_{3}(t)=\left\{\begin{array}{ll} 1+\cos (\pi t), & |t|<1 \\ 0, & \text { otherwise } \end{array}\right. (b) (6 points) Find the inverse Fourier transform of the signal shown below: (c) (8 points) Two signals f1(t) and f2(t) are defined as f_{1}(t)=\operatorname{sinc}(2 t) f_{2}(t)=\operatorname{sinc}(t) \cos (3 \pi t) Let the convolution of the two signals be f(t) = (f1 * f2)(t) i. Find F(jw), the Fourier transform of f(t). ii. Find f(t).