H(z) = (z2 + 0.5z - 0.5)/(z2 + 1.5z + 0.5)

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Homework Statement

Homework Equations

H(z) = Y(z)/X(z)

The Attempt at a Solution

I realized this wasn't in partial fraction form because the 1+z^-1+0.5z^-2 has non-real roots. I multiplied the 1st fraction part by z¹ and the 2nd fraction by z², then I combined them into one fraction and I think I am able to get a difference equation at the end, but is the way I am doing it right? Or is there an easier way to do this problem that I am missing.

 

[Hesch]

I multiplied the 1st fraction part by z1 and the 2nd fraction by z2, then I combined them into one fraction

Yes, that's how you do it.

H(z) = 1/(1+0.5z^-1) - 1/(1+z^-1+0.5z^-2) = z/(z+0.5) - z²/(z²+z+0.5).

Combine the fractions.