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## Homework Statement

Determine the stability of the following linear system

[itex]y(n) = 0.5x(n) +100x(n-2) - 20x(n-10)[/itex]

## Homework Equations

[itex]x(n) = 0.5\delta(n) [/itex]

[itex]S=\sum^{\infty}_{k=0}\left| h(k)\right|[/itex]

## The Attempt at a Solution

[itex]Z \left\{ 0.5x(n) +100x(n-2) - 20x(n-10) \right\} [/itex]

[itex] Z \left\{y(n) \right\} = \frac{xz}{2(z-1)^2}+100x(\frac{z}{(z-1)^2}-\frac{2z}{(z-1)})-(\frac{20x}{(z-1)^2}-\frac{10z}{(z-1)}) [/itex]

[itex] \frac{80.5xz}{(z-1)^2}[/itex]

Now at this point we were told that there should be a polynomial in the numerator... did I go about this all wrong? Any recommend reading would be helpful as I have exhausted Google searching for a similar problem.

My original approach was simply to take the geometric series and use each coefficient from this equation if the formula [itex]\sum\frac{1}{1-a}[/itex]

My result was [itex] \approx -.47 [/itex] which I though would be marginally stable as it is between -1 and 1.