(Solved):   3. A causal discrete-time LTI system is described by \[ y[n]-\frac{3}{4} y[n-1]+\frac{1}{8 ...

 

3. A causal discrete-time LTI system is described by \[ y[n]-\frac{3}{4} y[n-1]+\frac{1}{8} y[n-2]=x[n] \] where \( x[n] \) and \( y[n] \) are the input and output of the system, respectively. (a) Determine the system function \( \mathrm{H}(\mathrm{z}) \). (b) Find the impulse response \( h[n] \) of the system. [1+2 marks] 4. For a CT system represented by the following transfer function: \[ H(s)=\frac{s^{2}+5 s+2}{s^{2}+2 s+1} \] (a) Test the stability of the system. (b) Plot the pole-zero diagram. [1+1 marks]