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Math Help - Partial fraction expansion (z-transforms)

  1. #1
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    Question Partial fraction expansion (z-transforms)

    Hi,
    I have a function
    Y(z)= 1/(1-z^-1)^3,
    I used the convolution sum to get:-
    y[n]= 1/2(n+2)(n+1)u[n]
    But is it possible to expand Y(z) and evaluate y[n] directly using partial fractions or any other method?
    Cheers
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  2. #2
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    Apr 2010
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    Thumbs up

    In case any one is interested:-

    Using

    A/(1-dz^-1)^m <--z--> [A(n-1)...(n+m-1)d^n/(m-1)!]u[n] for ROC |z|>d

    which implies the answer is:
    y[n]= 1/2(n+2)(n+1)u[n]

    Can also be solved using the power series but harder to find a general representation..
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