(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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].

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transfer function to impulse response

**Physics Forums | Science Articles, Homework Help, Discussion**