Help me understand a Z transform

[diegoi]

Need help on Z transform

Need to know if this is a causal system

h(z)=z^-1/(z^-2+3z^-1+4)

 

[me2please]

Re: Need help on Z transform

\[r^{n}sin(\omega n)u[n] \Longleftrightarrow \frac{r sin(\omega )z^{-1}}{1-2rcos(\omega )z^{-1}+r^{2}z^{-2}}\]
causal when \[|z|>r\]

 

[usernam]

Re: Need help on Z transform

Hi,
Whether this system is causal or not depends on your ROC or region of convergence.
If you want this system to be causal then take a ROC |z|>0.5 and you will get
h[n]=0.18*{sin(0.7n)*(0.5)^n }u[n].
With this h[n] the system is causal.

 

[Mina Ayman]

Need help on Z transform

For more discussion on Z-transform illustrating the concept of causality, you can download the book at this site.
It contains an excellent chapter about Z-transform

 

[DrDolittle]

Re: Need help on Z transform

Please study "signals and linear systems" by bp lathi...but iam sorry i dont find that book downloadable anywhere.

Regards
drdolittle

 

[amarnath]

Need help on Z transform

it is simple.a causal system is a system whose output depends only on present and past inputs and not future inputs.just equate this to y(z /x(z) and find the inverse z transform .then u will find that the system specified is a causal system.in short the response of the system should be zero for n<0.where n is the time index.

regards
amarnaty

 

[snaider]

Re: Need help on Z transform

you can now that takin a review in any control book like the kuo , ogatta or the dorf, or if you wanna go deeper you can see any signal and systen book like the haykin or amdabar.