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## Homework Statement

Given the transfer function of a linear, time-invariant system

[tex]H(z)=\frac{z^2+5z}{z^2+5}[/tex]

compute the impulse response.

## Homework Equations

We are supposed to compute the inverse z-transform with partial fraction decomposition but the problem here is the irreducible quadratic function [tex]z^2+5[/tex].

## The Attempt at a Solution

In our table of inverse z-transforms they are only functions of the the type

[tex]\frac{z^{m+1}}{(z-a)^{m+1}}[/tex]

I tried this.

[tex]H(z)=\frac{z^2+5z}{z^2+5}=\frac{z^2}{z^2+5}+5\frac{z}{z^2+5}[/tex]

I can compute the inverse z-transform of [tex]\frac{z^2}{z^2+5}[/tex] just fine, but how do I compute the inverse z-transform of [tex]\frac{z}{z^2+5}[/tex]

Thanks.