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Z transform proof

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Using the definition of the z-transform, show that if [tex]X(z)[/tex] is the z-transform of [tex]x(n) = x_{R}(n) +jx_{I}(n)[/tex], then:
    [tex]Z\{x^{*}(n)\}=X^{*}(z^{*})[/tex]


    2. Relevant equations

    z-tranform definition:

    [tex]Z\{x(n)\}=X(z)=\sum x(n)z^{-n}[/tex]



    3. The attempt at a solution

    [tex]x(n) = x_{R}(n) + jx_{I}(n) \Longrightarrow x^{*}(n) = x_{R}(n) - jx_{I}(n)[/tex]

    [tex]Z\{x^{*}(n)\}=Z\{x_{R}(n) - jx_{I}(n)\}=\sum x^{*}(n)z^{-n}[/tex]

    [tex]=\sum [x_{R}(n) - jx_{I}(n)]z^{-n}[/tex]

    [tex]=\sum [x_{R}(n)z^{-n} - jx_{I}(n)z^{-n}][/tex]


    [tex]=\sum x_{R}(n)z^{-n} - j \sum x_{I}(n)z^{-n}[/tex]
     
    Last edited: Sep 23, 2011
  2. jcsd
  3. Sep 24, 2011 #2
    This is where I am stuck. Am I going in the right direction?
     
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