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Math Help - Questions related to limit

  1. #1
    Member moonnightingale's Avatar
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    Questions related to limit

    I am stuck with this question. I have to calculate the limit

    my formula is .. This is final value theorem of Z transform

    f(infinity) = limit (z-->1) [ 1- z^ -1] x [ 1/( 1+ z^ -2]

    How to solve this

    second is

    f(infinity) = limit (z-->1) [ 1- z^ -1] x [ z / (( z-1/2) (z-2))]
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  2. #2
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    Quote Originally Posted by moonnightingale View Post
    I am stuck with this question. I have to calculate the limit

    my formula is .. This is final value theorem of Z transform

    f(infinity) = limit (z-->1) [ 1- z^ -1] x [ 1/( 1+ z^ -2]

    How to solve this

    second is

    f(infinity) = limit (z-->1) [ 1- z^ -1] x [ z / (( z-1/2) (z-2))]
    Both limits as posted are equal to zero.
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  3. #3
    Member moonnightingale's Avatar
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    But the answer should not be zero,answer should be infinity atleast for second case.
    Kindly see it again
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  4. #4
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    Quote Originally Posted by moonnightingale View Post
    But the answer should not be zero,answer should be infinity atleast for second case.
    Kindly see it again
    Both limits as posted are equal to zero.

    If you don't like that answer then I suggest you go back and check the calculations that led you to the limits you posted.
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  5. #5
    Member moonnightingale's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Both limits as posted are equal to zero.

    If you don't like that answer then I suggest you go back and check the calculations that led you to the limits you posted.
    I am pasting the question

    Its solution for Inverse Z transform code is also pasted.
    num=[0 1 0]
    den=[1 -5/2 1]
    x=[1 zeros(1,10)]
    y=filter(num,den,x)

    If we solve it with inversion integral then answer comes to be

    2/3 [2^k - (1/2)^k]

    which mean it is ascending continuously
    Its initial value is zero which is correct but final value should be infinity

    The formula for final value is

    x(infinity)= limit (z--->1) (1-1/z) F(z)
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