I have a transfer function $$ H(z) = \frac{Y(z)}{X(z)} = 1 - 0.5z^{-1} \text{.}$$ I'm interested in zeros and poles. I know I need to adjust the function to $$ H(z) = \frac{\prod_i(z-n_i)}{\prod_i(z-p_i)} \text{.}$$ My attempt is as follows: $$ H(z) = z^{-1} (z - 0.5)$$ So I guess a zero is at $z = 0.5$. Is it correct? Moreover, what should I do with $z^{-1}$? Ignore it?
Thank you.