Answer Happy

dt2 dt2 dt 1 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 dy(t) + 10y(t) = dº r(t) + 8 da(t) ) + 15x(t). 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 h[n] = 21 = 2 sin ) cos( 5n) (n -] . 1. [4 marks] Sketch the discrete-time Fourier transform of h[n] over the radian frequency interval –a <W <. 2. [5 marks] Find the output y[n] of this system to the input: x [n] = {ción tejfn + ej? ein + bez an + že jgn +e-jſn te un - п 27 n 1 п 6 + že jen