# How to take z-transform of a function with an absolute exponent value?

Can you help me find the z-transform of the impulse response below:

$$h(n) = (\frac{1}{2})^{|n-1|} + (\frac{1}{2})^{|n|}$$

I know the z-transform of $$(\frac{1}{2})^{n}$$ is equal to: $$(\frac{z}{z-b})$$

• $$\ u(n)\$$ $$\\space\space\space\space\space\$$ for $$\ n>0 \$$
• $$\ u(-n-1)\$$ $$\\space\space\$$ for $$\n < 0\$$
$$h(n) = (\frac{1}{2})^{n-1}u(n) + (\frac{1}{2})^{n}u(n) +(\frac{1}{2})^{-n+1}u(-n-1) + (\frac{1}{2})^{-n}u(-n-1)$$