Consider a discrete-time system described by the following dierence equation.

y(n) = y(n1).24y(n2) + 2x(n1)1.6x(n2)

a. Find the transfer function H(z).

b. Find the zero-state response to the causal exponential input x(k) = .8ⁿ(n). This means that given H(z), we can calculate Y(z) and subsequently the output, y(n) with all initial conditions presumed to be zero. Hence the term, zero-state.