Final answer:
To find the z-transform of the given function, substitute the given values into the z-transform formula and simplify. The resulting z-transform is 2z / ((z - 0.8)² + 0.32).
Step-by-step explanation:
The z-transform of the given function is found using the formula:
X(z) = ∑ [x(n) * z^(-n)]
To find the z-transform of x(n) = 2(0.8)ⁿ cos(n/2) u(n), we substitute the given values into the formula and simplify. We can then find the z-transform as:
X(z) = 2z / ((z - 0.8)² + 0.32)