[amp_mcq option1=”|z| > 1″ option2=”|z| < 1" option3="(Real part of z) > 0″ option4=”(Real part of z) < 0" correct="option2"]
The correct answer is: B. |z| < 1
The z-transform of a unit step function is given by:
$U(z) = \frac{1}{1-z^{-1}}$
The region of convergence of a z-transform is the set of all values of z for which the z-transform converges. The region of convergence of the z-transform of a unit step function is a circle with radius 1 and center at the origin. This is because the z-transform of a unit step function is a geometric series with first term 1 and common ratio z-1. A geometric series converges if the absolute value of the common ratio is less than 1. In this case, the common ratio is z-1, so the z-transform converges if |z-1| < 1. This is equivalent to |z| < 1.
Option A is incorrect because the region of convergence is a circle with radius 1, not a circle with radius greater than 1.
Option C is incorrect because the region of convergence does not include the line (Real part of z) > 0.
Option D is incorrect because the region of convergence does not include the line (Real part of z) < 0.