Can the Z-Inverse Transform Be Computed Using the Residue Theorem?

[eljose]

Hello i would need some help to compute the Z-inverse transform of:

$$\frac{1}{z^{2}-1}$$ and $$\frac{1}{(z-1)(z^{2}-1)}$$

i don,t know if they can be computed using the residue theorem as the inverse in general has the form:

$$2\pi i a(n)=\oint f(z)z^{n-1}dz$$ for a curve on complex plane...

 

[HallsofIvy]

Why would you say that? It's not at all difficult to calculate the residues of $\frac{z^{n-1}}{z^2- 1}$ at z= 1 and -1 where the function has poles of order 1. Similarly for the residues of [itex]\frac{z^{n-1}}{(z-1)(z^2-1)}= \frac{z^{n-1}}{(z-1)^2(z+1)}[/itex\ at z= 1 and -1 with a pole of order 1 at z= -1 and a pole of order 2 at z= 1. Looks pretty easy to me.

 

[eljose]

Thanks..that was precisely the info i needed, if Z-inverse transform could be calculated by "residue theorem" if so i will try the functions above ..