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Math Help - Shifting from Laplace to time domian and then Z transform

  1. #1
    Member moonnightingale's Avatar
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    Shifting from Laplace to time domian and then Z transform

    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
    Last edited by moonnightingale; June 19th 2010 at 08:20 AM.
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  2. #2
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  3. #3
    Member moonnightingale's Avatar
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    Sorry it is Capital T
    I have corrected it

    exp(sT/2) / s^2
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  4. #4
    MHF Contributor chisigma's Avatar
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    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
    Last edited by chisigma; June 22nd 2010 at 01:22 AM. Reason: minor modifications...
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