Question

Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)].

(a) x(n)+y(n) ↔ X(z)Y(z)

(b) x(n)+y(n) ↔ X(z)+Y(z)

(c) x(n)y(n) ↔ X(z)+Y(z)

(d) x(n)y(n) ↔ X(z)Y(z)

This question was addressed to me in an interview for internship.

My question comes from Properties of Z Transform in division Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Correct option is (b) x(n)+y(n) ↔ X(z)+Y(z)

Easy explanation: According to the linearity property of z-transform, if X(z) and Y(z) are the z-transforms of x(n) and y(n) respectively then, the z-transform of x(n)+y(n) is X(z)+Y(z).