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Math Help - Z Transform for terms involving exp

  1. #1
    Member moonnightingale's Avatar
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    Z Transform for terms involving exp

    For many days i am unable to solve question regarding Z transform. kindly help me to calculate z transform of term which is having exp in it

    for example Z transform of [e^(sT/2)]/s^2or
    (e^(-1.5Ts))/((s+1)(s+3)) How to solve such questions. Kindly refer some book b/c my book does not explain it. ( s is laplace domain)

    Thanks a lot for ur help
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  2. #2
    A Plied Mathematician
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    Is the method Captain Black outlined in your other posts not going to work for these examples? If it is going to work, what do you get for the inverse Laplace Transforms?
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  3. #3
    Member moonnightingale's Avatar
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    Actually i dont dont do inverse laplace transform. I directly move from Laplace domain to Z domain through Lookup tables

    for example for
    1/s we can write z/(z-1)

    for 1/s^2 we can write Tz/(z-1)^2

    So i am solving all questions by this method and they are ok but only with exp terms i am stuck and
    and it is also required to be done same way.
    Can u eloborate capt black answer in simple words
    I am really stuck with this problem
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by moonnightingale View Post
    For many days i am unable to solve question regarding Z transform. kindly help me to calculate z transform of term which is having exp in it

    for example Z transform of [e^(sT/2)]/s^2or
    (e^(-1.5Ts))/((s+1)(s+3)) How to solve such questions. Kindly refer some book b/c my book does not explain it. ( s is laplace domain)

    Thanks a lot for ur help
    Multiplication by an exponential term in the s-domain is equivalent to a translation in the time domain, so what do that means for the z-domain?

    (If the delay were an integer multiple of the sample interval I would be happier, but I expect fractional sample delays are OK-ish)

    Are we now doing this differently? Why did your tutor go from the s to t to z domains if you are supposed to be using look-up tables for a direct s to t mapping?

    (Also look at the tables carefully, I bet there is an entry on the relationship between the z-transform of e^{\alpha s}f(s) and that of f(s))


    CB
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  5. #5
    Member moonnightingale's Avatar
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    Thanks Sir, Can u kindly spare some time and solve my second question in easy steps. it will help me a lot.
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