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Z Transform

  1. Oct 10, 2009 #1

    jpm

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    1. The problem statement, all variables and given/known data

    I'm trying to take the (two-sided, aka defined for all n) Z-transform of

    [tex]x(n)=sin(Bn)[/tex]


    2. Relevant equations


    3. The attempt at a solution

    What I tried to do was split x(n) into

    [tex]x(n)=sin(Bn)u(n)+sin(Bn)u(-n-1)[/tex]

    The Z transform of the first part of x(n) was found from a table. The z transform of the 2nd was found from the fact that the z transform of [tex]-sin(Bn)u(-n-1)[/tex] equals the z transform of [tex]sin(Bn)u(n)[/tex]

    [tex]X(z)=\frac{z sin(B)}{z^2-2zcos(B)+1}-\frac{z sin(B)}{z^2-2zcos(B)+1}[/tex]

    So the z transform is zero? Could this be?
     
  2. jcsd
  3. Oct 10, 2009 #2

    CEL

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    Remember that [tex]sin x = \frac {e^{jx}-e^{-jx}}{2j}[/tex]
     
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