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May 1st, 2016, 02:58 AM   #1
szz
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Math Focus: Calculus
Doubt with inverse Z transform

Hi,

I am not sure about an exercise I solved for Inverse Z transform..
Having

$\displaystyle X(z) = {6 \over (z - 3)}$

I solved as:

$\displaystyle {6 \over (z - 3)} = -{6 \over (3 - z)} = -{2 \over (1 - {z \over 3})} \Rightarrow -2(1/3)^n u[-n] = x[n]$

I deduce it from the time inversion property:

$\displaystyle
\begin{aligned}
x[-n] & \overset{\mathcal Z}{\longleftrightarrow} X(z^{-1})\\
u[n] & \overset{\mathcal Z}{\longleftrightarrow} {1 \over 1 - z^{-1}}\\
u[-n] & \overset{\mathcal Z}{\longleftrightarrow} {1 \over 1 - z}\\
\end{aligned}
$

but I am not totally sure.
Could someone confirm if I am right or wrong ?
Thank you in advance.
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