Let's say that I have a system $H(z)$. What is causal inverse and how do I compute the causal inverse of $H(z)$?


1 Answer 1


The inverse $G(z)$ of a system $H(z)$ is simply

$$G(z) = \frac{1}{H(z)}$$

The poles of $G(z)$ are the zeros of $H(z)$ and the zeros of $G(z)$ are the poles of $H(z)$.

$G(z)$ is only stable if the poles are inside the unit circle, which implies that for $G(z)$ to be stable, $H(z)$ needs have all it's zero inside the unit circle, i.e. it's minimum phase.

So if $H(z)$ is causal, stable and minimum phase, it's inverse is also causal stable and minimum phase.

  • 1
    $\begingroup$ $G(z)$ is not causal if $H(z)$ has more poles than zeros. Namely, $G(z)$ would then have more zeros than poles. One could compensate for this using a delay (poles at zero). $\endgroup$
    – fibonatic
    Aug 27, 2022 at 17:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.