0
$\begingroup$

Imagine I know that a system comprises two LTI subsystems $H_a$ and $H_b$ connected in parallel. Also, suppose that I can measure the impulse response of the whole system, $H_a \| H_b$, and the impulse response of $H_a$. Is there any way to find the impulse response of $H_b$?

I may be tired, but I think is not possible.

Improve this question
$\endgroup$
5
  • $\begingroup$ Yes you can calculate it! It all comes from the LTI property too. $\endgroup$
    – Engineer
    Nov 19, 2019 at 15:12
  • $\begingroup$ thank you Engineer!, I don’t think you can! You only know the composite response and that of one of the subsystems, how can you use that info to find out the other? You maybe right, but I don’t see how and that’s why I asked... $\endgroup$
    – julovi
    Nov 19, 2019 at 15:16
  • $\begingroup$ could you elaborate on “connected in parallel”. A resistor and capacitor are ideally LTI components and can be connected in parallel but that usage relates to circuit topology. One can also consider that parallel can describe where the composite impulse response is a sum of component impulse responses $\endgroup$
    – user28715
    Nov 19, 2019 at 15:32
  • $\begingroup$ Thanks Stanley, I’m not measuring electric components but acoustic IRS... $\endgroup$
    – julovi
    Nov 19, 2019 at 15:46
  • $\begingroup$ @julovi there are acoustic analogs to circuit components. $\endgroup$
    – user28715
    Nov 19, 2019 at 15:49

1 Answer 1

Reset to default
3
$\begingroup$

For a parallel system, the individual subsystems just add, so you simply have $H_{||} = H_A + H_B$ . That goes for both the transfer function and the impulse response, so you can simply do $h_b = h_{||} - h_a$

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thanks Hilmar! I got it now! $\endgroup$
    – julovi
    Nov 19, 2019 at 15:29

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.