milind Posted April 10, 2004 Report Share Posted April 10, 2004 Hello, 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. Quote Link to comment Share on other sites More sharing options...

mixos Posted April 10, 2004 Report Share Posted April 10, 2004 That means that step input is : | 1 , t>0u(t)= | | 0 , t<0 u(t) | 1 |-------------------------- |___________________ t 0Right?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? Quote Link to comment Share on other sites More sharing options...

milind Posted April 10, 2004 Author Report Share Posted April 10, 2004 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. Quote Link to comment Share on other sites More sharing options...

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