ZTransform for a non-causal unstable signal. How to make Mathematica gives correct result?
- To: mathgroup at smc.vnet.net
- Subject: [mg108198] ZTransform for a non-causal unstable signal. How to make Mathematica gives correct result?
- From: "Nasser M. Abbasi" <nma at 12000.org>
- Date: Wed, 10 Mar 2010 01:46:22 -0500 (EST)
Hello;
I am trying to find the Z transform using Mathematica for the signal
(-(1/2)^n)*UnitStep[-n - 1];
This signal runs backward, from n=-1 to - infinity. It is not stable. But
for |z|<1/2, the Z transform converges and can be found to be
1/(1- 0.5 z^-1)
Which is what I was hoping Mathematica to return, but it returns back zero !
In[32]:= Clear[f, n, z]
f = (-(1/2)^n)*UnitStep[-n - 1];
ZTransform[f, n, z]
Out[34]= 0
I did the derivation by hand, and here is a link. I do not think I made a
mistake myself in the hand derivation? but was hoping to use Mathematica to
verify it. but not sure how to let Mathematica return back the same answer
as I have.
http://12000.org/tmp/030910/ztran.htm
Am I missing something here? do I need to use some assumptions for
Ztransform? did not have to when causal signals?
--Nasser