I have a little problem computing the inverse of this signal:
$X(z) = \frac{(z-1)(z+\frac{3}{2})}{(z+\frac{j}{2})(z-\frac{j}{2})(z-\frac{1}{2})}$ $X(z^{-1}) = ?$
I know how to take the inverse, $z=z^{-1}$ and then multiply the brackets and so on... But my problem is the numbers in the brackets, $1, -\frac{3}{2}, \frac{j}{2}$, are poles and zeros of a Pole-zero plot of the sequence $X(z)$.
And I think I loose that information, don't I?