A discrete time system has impulse response $h (n) = a^{n} u (n + 3), | a | < 1$ , which one of the following is/are correct about system?

non-causal

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static

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memoryless

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stable

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Solution

The correct option is D stable
$h (n) = a^{n} u (n + 3), | a | < 1$

It is stable because $\sum_{n = - \infty}^{\infty} h (n) = \sum_{n = - 3}^{\infty} a^{n}$ is finite $[∵ | a | < 1]$

It is non-causal because $h (- 1) = a^{- 1} u (2)$
$h (- 1) = a^{- 1}$

which is finite

It is memory and dynamic system because h(n) is depending upon u(n+3)

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