Question

Consider a discrete system, if the input x(n)=(0.6)nu(n) and the impulse response h(n)=(0.9)nu(n),

(1) Find the z-transform of x(n) and indicate its ROC.

Answer 1

The z-transform of the input signal x(n) = (0.6)^n u(n) is X(z) = 1 / (1 - 0.6z^-1), with the region of convergence (ROC) being |z| > 0.6.

Step-by-step explanation:

The student has asked for the z-transform of the input signal x(n) = (0.6)^n u(n) and to indicate its region of convergence (ROC). To find the z-transform of x(n), we can use the formula for the z-transform of a causal geometric sequence which is X(z) = 1 / (1 - az^-1), where |z| > |a| for the ROC, assuming the sequence is right-sided. In this case, a = 0.6. Therefore, the z-transform of x(n) is X(z) = 1 / (1 - 0.6z^-1), and the ROC is |z| > 0.6.