Question

What is the z-transform of the signal x[n] = a^nu(n)?

(a) X(z) =1/z-1

(b) X(z) = 1/1-z

(c) X(z) = z/z-a

(d) X(z) = 1/z-a

This question was addressed to me during an internship interview.

This key question is from The Z-Transfer Function topic in chapter Digital Control Systems of Control Systems

Answer 1

The correct option is (c) X(z) = z/z-a

Explanation: By definition this is the basic example of the z-transform and the Z-Transform of the equation is calculated is z/z-a.