Shifting from Laplace to time domian and then Z transform

**moonnightingale** · Jun 19th 2010, 07:06 AM

I want to have Z transform of This function

It is in laplac at present

exp(sT/2) / s^2

can it be directly converted to Z transform or first i have to make in time domain by taking Laplac inverse and then taking its Z transform

**Ackbeet** · Jun 19th 2010, 07:13 AM

See here and here.

**moonnightingale** · Jun 19th 2010, 07:20 AM

Sorry it is Capital T
I have corrected it

exp(sT/2) / s^2

**chisigma** · Jun 21st 2010, 10:37 PM

Your approach is correct and we have...

$\displaystyle f(t)= \mathcal{L}^{-1} \{\frac{e^{s \frac{T}{2}}}{s^{2}}\} = t + \frac{T}{2}$ (1)

... so that is...

$\displaystyle \mathcal {Z} \{f(t)\} = T \sum_{n=0}^{\infty} (n+\frac{1}{2})\ z^{-n} = T\ \{ \frac{z^{-1}}{(1-z^{-1})^{2}} + \frac{1}{2\ (1-z^{-1})}\} = \frac{T}{2}\ \frac{1+z^{-1}}{(1-z^{-1})^{2}}$ (2)

Kind regards

$\chi$ $\sigma$

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