Question

If the region of convergence of x1[n]+x2[n] is 1/>|z|<2/3, the region of convergence of x1[n]-x2[n] includes:

(a) 1/3>|z|<3

(b) 2/3>|z|<3

(c) 3/2>|z|<3

(d) 1/3>|z|<2/3

The question was asked in an internship interview.

The above asked question is from The Z-Transform topic in portion Digital Control Systems of Control Systems

Answer 1

Right option is (d) 1/3>|z|<2/3

For explanation I would say: Region of Convergence is the region for which the values of the roots in z transform are lying in the function and ROC remains the same for addition and subtraction in z-domain.