Input x is the sampled signal vector, may have both AC and DC components. Output vector y should not contain any AC component.
Example:
Input x = [0 1 2] Output y = [1 1 1]
Amitava, it is fantastic that you are contributing problems, but you really need to spend more time specifying what the solution should do. The person solving is left needing to guess too much.
Definitely Agree with the cyclist. W/o example it is impossible to understand the task to achieve.