1. Determine, in closed form, the causal signals a[n], whose z-transforms are given by (a) 1 X(2) = 1+1.52 1 0.5%-2 (b) 1 X(2) = 1 0.52 +0.62-2 What are the ROCs? 2. Consider the system H(2)= 1-2-1+22-2-2-3 (1-1)(1 0.52-1)(1 -0.22-1)' (a) Sketch the pole-zero pattern. Is the system stable? (b) Determine the impulse response of the system 3. Consider the causal system ROC: 0.5|2|> 1 y[n]=ay[n-1]+ box [n] + bx[n-1]. Determine the (a) impulse response (b) zero-state response to a step input (c) step response if y[= 1] = A0 (d) Natural and forced response of the system to the input a[n] = cos(won], n≥0 4. Determine the zero-state response of the system y[n] = 0.5y[n 1] + 4x[n] + 3x[n-1] to the input x[n] = ejwon u[n]. (a) Is the system stable? (b) What is the transient response of the system? (c) What is the steady-state response of the system? 5. Show that the following systems are equivalent (a) y[n] = 0.2y[n-1]+x[n] -0.3x[n-1]+0.02x[n-2] (b) y[n] = x[n] 0.1x[n-1] -