1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - transform proof Date
Hilbert Transform May 1, 2016
Fourier transform convolution proof May 5, 2014
Statistics: variable transformation proof? Mar 3, 2014
Linear transformation proof Aug 15, 2013
Linear Transformation proof. Apr 16, 2013