0
$\begingroup$

enter image description here

I want to get impulse response of this causal system on first photo.

So I got frequency response on second photo from this system.

and now I am trying to transform this frequency response to impulse response on third photo.

but I can't invert it because there is a square of s on numerator.

How can I invert it to impulse response?

$\endgroup$
1
$\begingroup$

Several comments:

First, the usual symbol for the Z-transform is $z$ rather than $s$ (which is common for Laplace transform).

It is more common to express $H(z)$ in terms of $z^{-1}$. Note that the causal inverse transform for a single pole at $\alpha$: $H(z) = 1/(1-\alpha z^-1)$ is $h[n] = u[n] \alpha^n$.

So your transform $H(z) = \frac{3}{1 - 1/4 z^{-1} - 1/8 z^{-2}}$ can be expanded to the sum of two terms like the single pole above.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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