Answer Happy

Question 2 [25 marks]: Answer the following questions and upload your detailed solutions in Part C: a) The input signal 2(t) and the output signal y(t) of a linear time invariant (LTI) system are related by the differential equation: d’y(t) d>:(t) +10y(t) = +8 dz(t) + 15x(t). +7 dy(t) dt2 dt dit2 dt Y(jw) of this system. 1. [4 marks] Find the frequency response, i.e., H(jw) = X(jw) 2. [4 marks] Find the impulse response of this system. 3. [4 marks] Find the frequency response of the inverse of this system. 4.[4 marks] Find the impulse response of the inverse of this system. b) The impulse response of a discrete-time linear and time invariant system is given by sim( ")cos(an). пn h[n] = 21 1. [4 marks] Sketch the discrete-time Fourier transform of h[n] over the radian frequency interval -1 <W<. 2. [5 marks] Find the output y[n] of this system to the input: x[n] Lesõn +evtr +ejten + Levon +2e-jgn +e-jſn = + +e +