# z transform of a digital filter

Started by March 24, 2007
```hello!! I hope you can help me out.
I need to find the Z tansform from a Laplace expresi&#2013265923;n:

5(1-e^-sT)/s(s+1)(s+2)

Now, I know that there is a table to calculate this but I can't find
anything on the web, maybe you have one, or you'd know someway to solve
this, I really need it, I hope you can help me, thanks!

```
```On Mar 25, 7:39 am, "su" <macaroli...@yahoo.com.mx> wrote:
> hello!! I hope you can help me out.
> I need to find the Z tansform from a Laplace expresi=F3n:
>
>                5(1-e^-sT)/s(s+1)(s+2)
>
> Now, I know that there is a table to calculate this but I can't find
> anything on the web, maybe you have one, or you'd know someway to solve
> this, I really need it, I hope you can help me, thanks!

This 5(1-z^-1)Z(1/s(s+1)(s+2))
Where Z is the z transform operation.

```
```Hardy.Spicer@yahoo.co.uk wrote:
> On Mar 25, 7:39 am, "su" <macaroli...@yahoo.com.mx> wrote:
>> hello!! I hope you can help me out.
>> I need to find the Z tansform from a Laplace expresi&#65533;n:
>>
>>                5(1-e^-sT)/s(s+1)(s+2)
>>
>> Now, I know that there is a table to calculate this but I can't find
>> anything on the web, maybe you have one, or you'd know someway to solve
>> this, I really need it, I hope you can help me, thanks!
>
> This 5(1-z^-1)Z(1/s(s+1)(s+2))
> Where Z is the z transform operation.

Huh? What are those s's doing there?

Jerry
--
Engineering is the art of making what you want from things you can get.
&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
```
```On Mar 25, 9:43 am, Jerry Avins <j...@ieee.org> wrote:
> Hardy.Spi...@yahoo.co.uk wrote:
> > On Mar 25, 7:39 am, "su" <macaroli...@yahoo.com.mx> wrote:
> >> hello!! I hope you can help me out.
> >> I need to find the Z tansform from a Laplace expresi?n:
>
> >>                5(1-e^-sT)/s(s+1)(s+2)
>
> >> Now, I know that there is a table to calculate this but I can't find
> >> anything on the web, maybe you have one, or you'd know someway to solve
> >> this, I really need it, I hope you can help me, thanks!
>
> > This 5(1-z^-1)Z(1/s(s+1)(s+2))
> > Where Z is the z transform operation.
>
> Huh? What are those s's doing there?
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

It's for him to work out ie Z(1/s(s+1)(s+2)) is the z-transform of the
Laplace part leaving out 1-exp(-sT) which is the bit I am assuming he
had trouble with. I am not doing the whole calculation!

H=2ES

```
```su wrote:
> hello!! I hope you can help me out.
> I need to find the Z tansform from a Laplace expresi&#2013265923;n:
>
>                5(1-e^-sT)/s(s+1)(s+2)
>
> Now, I know that there is a table to calculate this but I can't find
> anything on the web, maybe you have one, or you'd know someway to solve
> this, I really need it, I hope you can help me, thanks!
>
>
vague, unsatisfactory question.

Unless you're willing to allow expressions with ln(z)/T, or unless you
specify your system more thoroughly, you can't get an exact
transformation between a Laplace model and a z-domain model.

If you want an approximation you need to share information about how

You can get an exact z-domain representation of a system that has a
plant as described above plus a sampling stage (such as an ADC) and a
hold stage (such as a DAC), but you have to specify what those stages
are, as well as your sampling rate.

--

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

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```On Mar 26, 5:27 am, Tim Wescott <t...@seemywebsite.com> wrote:
> su wrote:
> > hello!! I hope you can help me out.
> > I need to find the Z tansform from a Laplace expresi=F3n:
>
> >                5(1-e^-sT)/s(s+1)(s+2)
>
> > Now, I know that there is a table to calculate this but I can't find
> > anything on the web, maybe you have one, or you'd know someway to solve
> > this, I really need it, I hope you can help me, thanks!
>
> vague, unsatisfactory question.
>
> Unless you're willing to allow expressions with ln(z)/T, or unless you
> specify your system more thoroughly, you can't get an exact
> transformation between a Laplace model and a z-domain model.
>
> If you want an approximation you need to share information about how
>
> You can get an exact z-domain representation of a system that has a
> plant as described above plus a sampling stage (such as an ADC) and a
> hold stage (such as a DAC), but you have to specify what those stages
> are, as well as your sampling rate.
>
> give you a sensible answer.
>
> --
>
> Tim Wescott
> Wescott Design Serviceshttp://www.wescottdesign.com
>
>
> Do you need to implement control loops in software?
> "Applied Control Theory for Embedded Systems" gives you just what it says.
> See details athttp://www.wescottdesign.com/actfes/actfes.html

I assume he means that the (1-exp(-ST)/S is a zero order hold. In
control text books they include this a lot.
It's historical and goes back to the days when they couldn't sample
high enough and had to include it. Of course I suppose you need always
include it but it gets negligible the higher you sample.

H=2ES

```