# z transform

Started by May 4, 2011
```Hi everyone

I need help with how to transform T(s)=(omega^2)/((s(s+a))+(omega^2)).
Because I cant seem to find a similar equation in the z transform table.

Thank you

```
```On 05/04/2011 05:08 PM, saras3083 wrote:
> Hi everyone
>
> I need help with how to transform T(s)=(omega^2)/((s(s+a))+(omega^2)).
> Because I cant seem to find a similar equation in the z transform table.

That is an expression in the Laplace domain, which describes a signal or
a system's behavior in continuous time.

The z domain describes signals and system behavior in discrete time.

You cannot exactly express a continuous-time signal or a continuous-time
system with sampled-time signals or system descriptions.

Thus, there is no exact* transform between the Laplace domain and the z
domain.

I assume that you're showing a system transfer function.  There _are_
ways to make sampled-time systems that approximate the behavior of a
specified continuous-time system.  There are exact ways to model how the
behavior of a continuous-time system appears as 'seen' from a sampled
time system.  Look up the "bilinear transform" for one of the many
flavors of the former -- I'm not sure what the name is of the latter.

* Well, sorta kinda no exact transform -- if you know enough
sampled-time signal processing theory to argue with me, you don't need
to read any of the above.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```>I need help with how to transform T(s)=(omega^2)/((s(s+a))+(omega^2)).
>Because I cant seem to find a similar equation in the z transform table.
You can use the bilinear transform by setting s = 2/T * (1 - z^-1)/(1 +
z^-1) then cranking to get the numerator and denominator into powers of
z^-1.  T is your sample period, of course.

Mark

```