Answer Happy

( = dt = 1 Answer the following questions and upload your detailed solutions in Part C: a) The input signal x(t) and the output signal y(t) of a linear time invariant (LTI) system are related by the differential equation: d'y(t) + 7 dyt) + 10y(t) d? :(t) do(t) + 8 + 15x(t). dt2 dt2 Y(jw) 1. [4 marks] Find the frequency response, i.e., H(jw) of this system. 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 n) h[n] = 20 = 2 sin(Tr)] cos(5n). ) 1. [4 marks] Sketch the discrete-time Fourier transform of h[n] over the radian frequency interval –a <W < T. 2. [5 marks] Find the output y[n] of this system to the input: æ[n] = {eign tegn + ejten + Beton + }e-jan x + + {e-ign tejgn te jen jön + }e in = πη 5л п 5л п = junio