Assume you are given an LTI system with a step response s(n), which is defined as the output of the system when excited with (input) a step function u(n)? Can you derive the expression for the output y(n) in terms of s(n) and an arbitrary input x(n)?

Explanation:

Given:

is the step of response with LTI system.

and, It response h(n) then relates to phase response as,

Therefore, for the arbitrary input, the output is converted to .

So, put the value of that is .

Finally, open the bracket and multiply in the equation.

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