0
$\begingroup$

I have the ROC of a signal $x[n]$ with $z$-transform $X(z)$ as below: enter image description here

Now I am wondering how I can find $x[0]$ by not calculating inverse z transform based on the roc, I am looking for a simpler, and faster way.

$\endgroup$
0

1 Answer 1

1
$\begingroup$

I find the answer: initial value theorem, which states that $$\lim_{z\rightarrow\infty} X(z) = x[0]$$

$\endgroup$
1
  • $\begingroup$ Nice! Now all you have to do is find the expression for X(z). If you have trouble with that, happy to help ;) $\endgroup$
    – Jdip
    Oct 18, 2022 at 0:17

Your Answer

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

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