How to analyse anti-causal discrete transfer function using matlab?
The transfer function
$$H(z)=-z^{-2} -2z^{-1} +2z +z^2$$
can be written as
$$\begin{align}
H(z)&amp;=z^2z^{-2}\left(-z^{-2} -2z^{-1} +2z +z^2\right)\\
&amp;=z^2\left(-z^{-4} -2z^{-3} +2z^{-1} +1\right)\\
&amp;=H_1(z)H_2(z)
\end{align}$$
 It can now be seen more easily that


$H_1(z)$ has two zeros at $z=0$ (and two poles at $\pm\infty$) .
$H_2(z)$ has four poles at $z=0$ and four zeros: one at $z=1$ and three at $z=-1$. What can be said about pole-zero map of $H(z)$ overall?
Since $|H_1(e^{j\omega})|=1$, we cnclude that $|H(e^{j\omega})|=|H_2(e^{j\omega})|$
Since $\angle H_1(e^{j\omega})=2\omega$, we cnclude that $\angle H(e^{j\omega})=\angle H_2(e^{j\omega})+2\omega$