# Z transform proof

1. Sep 23, 2011

### SpaceDomain

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

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

2. Relevant equations

z-tranform definition:

$$Z\{x(n)\}=X(z)=\sum x(n)z^{-n}$$

3. The attempt at a solution

$$x(n) = x_{R}(n) + jx_{I}(n) \Longrightarrow x^{*}(n) = x_{R}(n) - jx_{I}(n)$$

$$Z\{x^{*}(n)\}=Z\{x_{R}(n) - jx_{I}(n)\}=\sum x^{*}(n)z^{-n}$$

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

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

$$=\sum x_{R}(n)z^{-n} - j \sum x_{I}(n)z^{-n}$$

Last edited: Sep 23, 2011
2. Sep 24, 2011

### SpaceDomain

This is where I am stuck. Am I going in the right direction?