inversed Z Transform

inzaghina · #1 $Old$ November 1st, 2009, 07:05 AM

Hello!
I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

z/(z^2+z+1)

and

z^2/(z^2+z+1)

Thank you in advance.

bkarpuz · #2 $Old$ November 1st, 2009, 02:53 PM

Quote:

Originally Posted by inzaghina $View Post$

Hello!
I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

z/(z^2+z+1)

and

z^2/(z^2+z+1)

Thank you in advance.

You should probably factorize.
Also you may refer to Mathematica 7.0 - InverseZTransform.
As a little note, if $\lim\nolimits_{z\to\infty}F(z)/z\neq0$ , then we can not find an exponentially bounded sequence $\{f(n)\}$ for which [math]f(n)=Z^{-1}\{F(z)\}(n)[\math] holds.

inzaghina · #3 $Old$ November 2nd, 2009, 05:34 AM

Well, I have to do that by hand, not in the computer.
And I did a mistake, I have to solve Z^(-1) of :

z/(z^2+z+1)^2

and

z^2/(z^2+z+1)^2

have a good day!

CaptainBlack · #4 $Old$ November 2nd, 2009, 06:36 AM

Quote:

Originally Posted by inzaghina $View Post$

Hello!
I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

z/(z^2+z+1)

divide top and bottom by $z^2$ to get:

$\frac{z^{-1}}{z^{-2}+z^{-1}+1}$

then look this up in a table of inverse z-transforms (item 18 in the table in the Wikipedia article on the z-transform looks like what you need)

CB