Question

Let x[n] = (1/-9)ⁿ u(n) - (- 1/3)ⁿ u(-n - 1). The Region of Convergence (ROC) of the z-transform of x[n]

(A) is |z| > 1/9

(B) is |z| < 1/3

(C) is 1/3 > |z| > 1/9

(D) does not exist.

Answer 1

Given x[n] = (-1/9)n u[n] - (-1/3)n u[-n - 1]

for (-1/9)h u[n] R_oc in |z| > 1/9

(Right sided sequence, R_oc in exterior of circle of radius 1/9)

Thus overall R_oc in 1/9 < |z| < 1/3