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Determine whether the following systems are stable or not y(n)=3x(n).
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Solution:

Let x(n)=δ(n),y(n)=h(n)

h(n)=3δ(n)

Condition for stability,

k=|h(k)|<

k=|h(k)|=k=0|3δ(k)|=k=03δ(k)=3δ(k)=0 for k0 and δ(k)=1 for k=0k=|h(k)|< the given system is stable

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