Jump to content
Electronics-Lab.com Community

What is the impulse response?


Recommended Posts

I have a question regarding Network Analysis.
Suppose we are given that the response to a step input at t=0 to a network is given as say
i(t) = -2exp(-t) + 4exp(-3t)

Then what is the impule response of the network and how can it be calculated??
Any suggestions are welcome.

Link to comment
Share on other sites

That means that step input is :

| 1 , t>0
u(t)= |
| 0 , t<0

1 |--------------------------
|___________________ t


Your system is this:

INPUT : x(t)= u(t)
OUTPUT : y(t)= impule response (unkown?)

The relation between them is y(t)=h(t)*x(t)

but h(t) can't be calculated easily right away... so you work at the frequency domain, where:

INPUT : x(s)= L [u(t)] -> x(s)= 1/s (where L is Laplace tranform)
OUTPUT : y(s)=H(s)*x(s)

So IF you know (or can calculate) H(s) of your system then you can find y(s) becuase x(s)=1/s. Finally making reverse Laplace transform (L^-1) of y(s) you can find y(t) which is the IMPULSE RESPONSE:

y(t) = (L^-1)[y(s)]

Do you know H(s) or can u calculate it for your system?

Link to comment
Share on other sites

Well as I wrote here i(t) (given by me) is the response to u(t) therefore

i(t) = u(t)*h(t) where h(t) is the impulse response, so we can calculate h(t) in the frequency domain as:

H(s) = sI(s)

but this creates a confusion since if the response of u(t) is i(t) the response to D(t) (A unit impulse = du(t)/dt ) should be di(t)/dt which becomes in the s domain as:

sI(s) - i(0+) hence we get 2 different answers.

Stretching this to the basics we have Laplace of u(t) = 1/s so the Laplace for a unit impulse D(t) should be (from the differentiation rule) = s.(1/s) - u(0+) = 1 - 1 = 0. But its simply taken s.(1/s) = 1.
Why is this? Any help would be appreciated.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

  • Create New...