x ' t) = sin (t) 1. (1) Calculate the Fourier transform (X(jw )) of x(t): Hint: x(t) can be re-written as the format of sinc function and its Fourier transform can be found in a table . (2) Determine w , such that for arbitrary | w | > w, , X(jw)=0. (3) Determine the minimal angular frequency w, that satisfies Nyquist sampling theorem. (4) Determine the output y(t), after x(t) goes through the filter F(jw ) has the following characteristics in Fourier domain. F (jol = 1;@ =2 10; elsewhere (5) Determine the output y (t), after x(t) goes through the filter F (jw ) has the following characteristics in Fourier domain. F (jol = 1;2 =10 =3 0; elsewhere 2. Consider a time invariant linear system y(t)=H[u(t)]. The impulse response of the system is h(t)=e tu(t) (u(t)=0 for t