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Math Help - Help is required for Z transform

  1. #1
    Member moonnightingale's Avatar
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    Help is required for Z transform

    I have to calculate Z transform of following equation

    e^x/s^3 where x = sT/2 ( I could not write in latex in direct equation thats why i am showing x)

    Kindly show me all steps
    Thanks
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  2. #2
    A Plied Mathematician
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    Just to clarify, you're required to compute the Z transform of the function \frac{e^{s T/2}}{s^{3}}. Is that correct?
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  3. #3
    Member moonnightingale's Avatar
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    yes absolutely right
    kindly show me all steps to solve this problem
    Thanks
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  4. #4
    A Plied Mathematician
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    One more clarification: I'm assuming that s is an integer. Correct?
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  5. #5
    Member moonnightingale's Avatar
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    No s is not an integer
    s is basically Laplace domain.
    Basically this is in continuous time and i have to make it in discrete form for which i have equation
    In that equation i have to perform Z transform. of it. then i will move from laplace domain to z domain

    Kindly avoid moving from Laplace to time domain and from time domain to z domain
    This question is required to be solved directly from Laplace domain to Z domain
    Thnnks
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  6. #6
    Member moonnightingale's Avatar
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    I am also uploading the solution of instructor but i am unable to understand it

    Kindly this to me or if u have got some easy solution that will be more convenient for me
    Attached Thumbnails Attached Thumbnails Help is required for Z transform-solution.jpg  
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  7. #7
    A Plied Mathematician
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    I feel like I'm missing something here. Could you please state the original problem, word-for-word? Thanks!
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  8. #8
    Member moonnightingale's Avatar
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    Nothing is missing
    I just have to find Z transform of this
    e^x/s^3
    where x = sT/2 ( I could not write in latex in direct equation thats why i am showing x)
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  9. #9
    Grand Panjandrum
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    Quote Originally Posted by moonnightingale View Post
    I am also uploading the solution of instructor but i am unable to understand it

    Kindly this to me or if u have got some easy solution that will be more convenient for me
    What you tutor appears to have done is take the inverse LT of G(s)/s, sampled it and then taken the ZT of what resulted (I am assuming that their work is correct).

    CB
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  10. #10
    A Plied Mathematician
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    Many thanks to CB for that illuminating post.

    There is an error in your tutor's calculations. Everything is correct up until the last line, which should be the following:

    \frac{T^{2}}{2}\left[\frac{z(z+1)+z(z-1)+0.25\,z(z-1)^{2}}{(z-1)^{3}}\right].
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  11. #11
    Member moonnightingale's Avatar
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    I am unable to understand. Can anybody explain this to me with other simple method
    Thanks
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  12. #12
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    Well, your tutor's method of solution is precisely what CB said it was. That is evidently the method of solution desired. I'm not sure there is a simpler method. The substitution z=e^{sT} does not appear to coincide with your tutor's method. I'm not sure I understand why. Does CB have any ideas?
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  13. #13
    Grand Panjandrum
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    Quote Originally Posted by Ackbeet View Post
    Well, your tutor's method of solution is precisely what CB said it was. That is evidently the method of solution desired. I'm not sure there is a simpler method. The substitution z=e^{sT} does not appear to coincide with your tutor's method. I'm not sure I understand why. Does CB have any ideas?
    This cannot work for an arbitrary signal as it would imply the equality of a sum dependent on the signal values at the sample points and an integral dependent on the signal at all (positive) times. That these cannot be equal is clear as the value of the integral can be altered by altering the signal between sample points leaving the sum unchanged.

    It does map the LT of the signal multiplied by a comb of deltas (iirc) to the ZT of the sampled signal.

    CB
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