Unit step response of the system described by difference equation y(n) + y(n - 1) = x(n) is

Concept:

1. Analysis of continuous-time LTI systems can be done using z-transforms.

It is a powerful mathematical tool to convert differential equations into algebraic equations.

2. The bilateral (two-sided) z-transform of a discrete-time signal x(n) is given as

3. The unilateral (one-sided) z-transform of a discrete-time signal x(n) is given as

4. Time shifting property of Z transform

x(n - 1) = z-1x(z)

5. Z transform of u(n)

Calculation:

Given,

y(n) + y(n-1) = x(n)  ----(1)

Now finding unit step response of equation (1) using above properties we get:

Hence option (1) is the correct answer.