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if we have LTI system and we know unit step response of this system(we haven't original signal) how we can calculate impulse response?

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You can find the impulse response

Let's take the case of a discrete system.

If $s[n]$ is the unit step response of the system, we can write

$$s[n]= u[n]\ast h[n]$$

where $h[n]$ is the impulse response of the system and $u[n]$ is the unit step function.

Now using commutative property you can write $$s[n]=h[n]\ast u[n]$$

Expanding convolution we get $$s[n] = \sum_{k=-\infty}^{\infty}h[k]u[n-k]$$

which can also be written as

$$s[n]=\sum_{k =-\infty}^{n} h[k]$$

So we can see that unit step response is like an accumulator of all value of impulse response from $-\infty$ to $n$. So now impulse response can be written as the first difference of step response.

$$h[n]=s[n] - s[n-1]$$

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