(3) Consider a causal filter with the transfer function: H(z) = k(; 1-2-2 1+α12-1 + a2z- ), where k 0.136728736, a₁ = 0.53353098, a2 = 0.726542528 (a) Find the poles and zeros of the filter. Check for stability. find and plot the magnitude response of the filter. What type is it? (b) Determine the steady-state of the filter if the input is given by: x(n) = 2u(n) + 2cos(0.6n+)u(n) – 5cos(x)u(n). (c) Find expressions for the steady-state and transient responses if the input is a step u(n). Hence, plot the transient response. (d) determine the duration of the transient response and the energy of the transient response.