1) A discrete-time, causal and LTI system is shown below. x[n] and y[n] are input and output signals of the system. 3 -1]- - y[n a) Find the system function, H(z), and the impulse response, h[n]. b)...

Extracted text: 1) A discrete-time, causal and LTI system is shown below. x[n] and y[n] are input and output signals of the system. 3 -1]- - y[n a) Find the system function, H(z), and the impulse response, h[n]. b) Find the step function, s[n], of the system. (Hint: if x[n]=u[n], y[n]=s[n]) -1 c) Find the z-transforms of the signals x[n] = n u[n- 2] and x[n] = u[n – 1] u[n] using the properties of the z-transform. Write the results as the functions of X(z). d (Hint: nx[n]<→-zx(2))>