The output y[n] of a discrete-time system for an input x[n] is y[n]=\max _{-\infty \leqk \leq n}{|x[k]|} The unit impulse response of the system is Option

Correct Answer is : unit step signal u[n]

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 22 of 65

Marks: +1, -0

The output

y[n]

of a discrete-time system for an input

x[n]

y[n]=\max ↙{-∞ ≤k ≤ n}{|x[k]|}

The unit impulse response of the system is Option

Solution:

{Y}( {n})=\max ↙{-∞ ≤ {K} ≤ {n} }[x(K)]

{Y}( {n})=\max [δ( {K})]=1-∞ ≤ {K} ≤ {n}

{Y}( {n})

is 1 for all

{n}

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