The output y-n- of a discrete-time system for an input x-n- isy-n- k - nmax-x-k-The unit impulse response of the system is

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The output y[...

Question

The output $y [n]$ of a discrete-time system for an input $x [n]$ is

$y [n] = max - \infty \leq k \leq n | x [k] |$
The unit impulse response of the system is

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X (z) = 1 = 3 z^{- 1},

Y (z) = 1 + 2 z^{- 2}

δ [n - 1]

y [n] = \sum_{k = 0}^{n^{2}} c o s (\frac{π}{4} K) x [K]

x (n) = {(\frac{1}{2})}^{n} u (n) - \frac{1}{4} {(\frac{1}{2})}^{n - 1} u (n - 1)

y (n) = {(\frac{1}{3})}^{n} u (n)

(2 δ [n + 1] + δ [n] + δ [n - 1])

[{(\frac{1}{2})}^{n} u [n]] \cdot

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